Transcript for:
Overview of Numerical Functions

In the name of God, the Most Gracious, the Most Merciful, and peace and blessings be upon him Welcome to the Messenger of God, my sons and daughters, all of them Second secondary school, experimental sciences, technical mathematics And the athlete in this video, God willing, will We are talking about the axis of numerical functions, which is The first axis is one of the most important axes in the first My daughters and I only recommend this book to you. The second edition has everything, including lessons. Detailed practical exercises, eighty training sessions And tests in it 134 tests and everything is attached with its title on YouTube means this exercise is solved. Here it is. The exercise solution for those who did not understand anything He tells you his address on YouTube, write this The address on YouTube shows you Professor Nour Religion explains the same exercise to you with sound and picture We are going to talk about the lesson function definition group With applications we will talk about the equality of two functions Lesson with applications and intensive Algebraic Operations on Functions Lesson with Applications The composition of the functions, which is a sensitive element, is gone. We talk about the lesson and many applications. How do we get it? The definition set is specific to the compound of two functions. The direction of change of functions we talk about is f plus k. Honda VF and Gear F, special installation is available People make mistakes in how to study complex direction. We also have two functions with graphical representations. We summarized the whole thing in a table that shows all the cases and that's it. We also made the table here in the release. This is here on the page, fully explained in detail. We also have teacher change constitutions, including: Axis and Center of Symmetry Lesson with Applications and Rani We recommend you this math book called A to Z, the second edition, is here All you need Profit Now you have to bring a notebook and a pen and don't tell me The video is long because it has a lot of things going on. Let's start. Now in the detailed explanation point by point and the leader His leader let me comment when he finishes the video The professor told me that I have completed it, God willing. He answers, completes it, answers 20 out of 20. We try to take off. Now in the explanation we come now to the detailed explanation Point by point, my boys and girls, but we want you to be patient. On the video and try to understand it point by point Point because this lesson is important because in the beginning I would like to talk about a reminder about functions that are Tribal gains, meaning you learned them in your lifetime The first of them is the function and the definition set. The one you were referring to, BDF and DJ said Definition: It is part of the set of real numbers. If this is a group, it is a definition group. The function fvanx is associated with every real number x. From DF a unique real number we symbolize BAF Y X means this is how we go from here to F Lax, through a function called AF, follow me well We say that f lax is the image of the number x. With the function F, the correct set of the definition of the function F is The set of real numbers x of which This is an FLX account. Can you focus on this with me? We understand from this note that DF is a field or Federation of domains means this definition set. We appreciate her share, Mama's share is the union of Ta' Fields We have important notes that must be taken into account. It is not non-existent, meaning it is like a relative who is broken. The position is not non-existent, you have read it, but The expression under the square root must be Positive Oh, we will not break the camel's back a lot, maybe a group This definition tells you that I do not understand this exercise. The application that made us understand everything correctly is an exercise. The application, what did we say, and I told you, Eye DF Function definition set F in each condition We start with health. We start with the first case if We said DF TSA SHOW We see that this function has no denominator. It does not contain a direct root. The definite article group is understood. Hi, I was wondering if we could write in the form of a field. From the infinity minus or we write this limit Manieh Shatar the second one also DF is equal to us Professor, there is a position, but this position is now Seven is not a variable, it is impossible for it to equal zero. Directly, this is number two. We said number one, now we come to number Three DF equals us, this is not a break here Cake even if the absolute value is not affected absolute value like that Ark The quarter RDF equals see Mayadi, there is no normal fracture here, but we said When the denominator contains this variable x The denominator must be different from zero. This x means it is not equal to zero since it is not Equal to zero we say Ar star word ar najma means we don't shower zero I woke up, let's go to, for example Fifth, fifth, also DF equals us the same The scenario is that these two x's must not equal each other. Zero, I noticed that many people make mistakes and say: X is not equal to minus where no no we want to divide by Two by two becomes me X no It equals zero, which means it becomes my star as well. We don't want you to worry, we'll go now the condition 6th DF We are equal, sir. We have the root, but this The root is not a variable. The root of three is a value. Fixed, who should be in charge? It is not meaningless X not minus 4 not equal to zero Nadi this from My X is not equal to 4, that means We say all numbers Except The quarter means that all the numbers have pictures. By the way, the fourth one is not healthy Let's go further, you clever ones. Seventh If This is equal to no problem, so this is what it is. The denominator is not equal to zero. Let's see what we can do. This is from Sobhi, x squared does not equal 4 and from it x does not equal square root or x does not equal minus square root His friends, how much he is worth to us, he is worth to us, and this We are equal to minus a, what does it mean? What does it mean? X It's not worth two or three, sorry It is not equal to minus a, so we say Aar except for the missing one, where and two look at the complex This is a group of definitions that mean the thing that I lost my place, we will not accept it anymore We also go to the case The seventh DF is equal to. See with me and I have this. We said the position is not equal to the seventh case, sorry. the condition The eighth is that the denominator is not equal to zero, but we like it. This is what we said is two x squared plus one It is not equal to zero here Don't worry, this is necessary, this is necessary, this is necessary Positive is impossible equal to zero. Samsh will bring us back. The definition group has been very noticeable to me and my daughters. He tells you that the definition group is an empty group, no. No, all numbers. Any number you can substitute here is impossible. It equals the word "every" A number is a number we say every number that achieves a number we mean by it So you understand that when we move forward, we are now leaving. to Ninth, ninth Also DF where is the absolute value Lax minus three does not equal zero That means the denominator is not always equal to zero. We go back. In this case the denominator is not equal to zero value The divorced woman should be like this. We can do whatever is easy for her. Good morning, x minus three does not equal zero We return this from my morning X does not equal three so that You have the absolute value alone that you can appreciate. Delete it immediately. It doesn't matter. Just tell me. My father's phrases It doesn't matter what happens to us, DF Except for the three, it's excellent. We're also going now to... the condition The nest is DF where the sh is where the place is absolute value Lax minus three is not equal to zero. We calculate this. The absolute value of x is not equal to three. We go back to Bermani and the properties of the one who saw me put it in Here is this version, I did not say the second version Who It means the book is the pinnacle of this second edition. We recommend you to say something different than what you said on the first page. Which is page 11, these are the properties of absolute value How much is it? Here is the famous match True, the absolute value is equal to a positive number, so either x no equals or x does not equal minus You wanted to make up for it? Here, 3 minus 3 zero Minus in absolute value is 3 3 minus challenge If all real numbers are equal to ∠, check ∠. The imperfect Three and three That one Excellent, let's keep moving forward Now to the eleventh DF Where what is inside the root is under the root The square must be positive, that is, this is the one It is x minus one, it must be positive, not Completely positive, completely positive. We transfer this from me to you. X is greater than or equal to one Its meaning is its meaning, from one who is more than me, its meaning is This is the field that we are talking about. This becomes mine. If We are equal One plus infinity is the sum Definition: We knock on this, oh here we love you to focus I have a lot of money here The denominator is called the square root. It is not equal to zero and the square root is not inside it Positive means how can we get this? 12 Excuse me We say DF where where two x minus Three is not equal zero And x minus two is not greater than or equal to what Inside the root is positive and what is in the denominator is different from Zero between them is a letter, which means what we mean by it Intersection Healthy, Nady, this is from this, you become two X's, no We are equal to three and we have an X, no greater than or equal to We are equal to two of them here, their daughters, and they always greet me. We divide by 1, 2, and 3. My morning is x, which does not equal three. On two And a bigger or equal weight Two and a word, and they always intersect. Souls We run this one and a half, this is zero, one and a half This is three divided by two, meaning all values ​​are achieved. Except this, this achieves. Except this, no. No, but the dozen is a field The second of two plus this is one and a half Two, this is one and a half, and we go, plus what not End and behind the intersection of the fields Ra Mth two Plus, don't become a DF equal to us Two plus m end this is the idea I like Intersecting fields to get a root with this thing We go now to the case 13 DF This is the view of the Sines function and this We studied the Cossence function in the first year. This is knowledge on R and this is knowledge on R if Their identification group is this, this, this, this. The intersection of the weld gives us only the R. Add here. Now we have learned this reminder about this lesson. The important thing is that I said the numerical functions, which is The first axis, then my sons come to Operations on functions where we talk about equality Daltin and Rani Daer here is the lesson with exercises In this second edition, note with me that we read Definition: The statement about the two functions F and G is that they are: Equal means they have the same set. Definition D1 for every real number x From this group, DNA Lax is equal to us. X, listen to Mia. What do we understand? Two functions are equal. If they have the same definition group and phrase The first is equal to the second expression, and we write F. Now let's move on to the practical exercise. We will understand everything for the first time in Algeria The book that will make a difference in your study of the subject Mathematics in the second year of secondary school book Explained in detail, page by page, in the easiest way. Free on Professor Nour El Din's channel The second book of the silver series, everything You need it in one book. Study with ease and confidence. Be among the top students in all Algerian states Prepared by Professor Nour El Din in cooperation with With Akasha team, order it from the nearest library From you, Akasha Library is more than just a publishing house. Akasha's books complete his joy The baccalaureate told me to remember if F was equal to In any case, we come now to the case First, if lax equals x plus two. Since this phrase is free of roots and Fractions Van d F Ra equals Li R directly Now come to me, DJ, so that I can... The matter is root, we said what is inside the root must If it is positive, we transfer this here and it becomes my X. Greater than or equal to us from minus where with us it becomes mine My children, this is what we read, we read it from the lacking Two plus infinity see the set The first definition is AR and the second is from the missing letter A Plus infinity becomes about us DF La DJ equals IF is not equal to G only Adi this is what it means They took off what is wrong with him. Where is this statement? It is true. These and these expressions are equal because any root of Ki His quarter goes to the root, meaning it becomes mine, this becomes mine It's the same as x plus two and this is x plus Two phrases how how does this condition mean Check but the first condition is not met click directly However, the function F and the function G are different. Equal, then we come to the example, my sons. The second also if we come now we know they heard Mia Malih Rana in the second, anything square below The root is known as R, which means DF Ray. We are equal, why, Professor? NX minus one All square under the root we said what is inside the root This must always be positive. Whatever number we put here, we replace it with any number here. This value remains positive if the group allows it. The first definition is how much is it and this is its value Absolute value is defined on the basis of AR as well. He is a Digi Ra, and this is the first condition for us. Check out the definition group How do we go now? To the phrases we have for X that All X from RNF LAX, this is my favorite I read in the first year that x squared under the square root It is the same absolute value. Lax also this is since the square with the root Okay, let's say he goes to the library, but this is not how it is How here the square is inside and here the square is outside Okay, how, how, if this book is the same, I would like it X by value X minus one and this is my opinion GLX is equal to us We think the condition is that the husband has the right to have a ... The same phrase, if we said this is how it should be The square goes to the square and the absolute value comes back This morning we are going to make DFDF equal to DF Digi phrase if equals us phrase come say and from it [music] The second case is equal. We go. Andy to the case The third third case what Hurry up, notice here that since Kane broke the denominator is necessary Not equal to zero means DF where the value is The absolute value of x is not equal to zero, which means that D You will make us do it Where is this position absent? Where is this position absent? Zero cm we said in the definition group when We talked and said that the denominator must not be equal to zero. It is different from zero and the root inside it is positive Oh Drook, this is her profile picture. but Digi complex definition of it Wherever you become me Are not equal to us are star definition group We are tormented and tormented differently, we say and from it, “Ugh, it is not equal.” Survivor means that both conditions must be met. The definition set is equal to the same and the phrases Different able equal phrases and group This definition is different directly, that the two functions not Equally, we come to the fourth case. But it has a kind of Focus first we come to what we say in The fourth DF, so that it is here with us Two conditions first what is inside The root is positive, not negative. What is in the denominator is the root of x Minus one is not equal to zero. We talked and we will talk again. We repeat if it was I have a root that must have a positive inside it. I had a fraction with a denominator other than zero, right? We transfer this from us and what happens to my children happens to me The square root of x does not equal one with x. We said it is positive. Because the root squares both sides and becomes x One is equal to the other. See with me if... We said here that the first case is zero, and x is positive. Na x is positive if we say so teacher Here we have an X that does not equal one, so we go Here is one whose meaning is complete and valuable. And this now realizes what the definition set becomes. My definition group is the intersection of colors becomes LD F equals us from zero to one union of One plus infinity, focus with me carefully This is DF We go now too Digi huh here DJ means DJ, this is the example Hail must be what is inside the root positive The position is different from zero. We transfer this from us to become I have an X that is not equal to us One of the same scenario will happen to me DJ Sh Tasawna Audi Mama Tahna Hanah X It differs from one and is greater than or equal to morning Digi from scratch One is the union of one plus infinity. Okay, listen to Mia's introduction group. Ugh and G came out equal, that's right here Click we don't click nd If you make us equal But is the condition met? Is this still true? Now we have for every x This phrase belongs to our DNA. Yes, every X of our DA is Effex this phrase we multiply it by the facilities what is it Its facilities, see with me the phrase, my opinion One over the square root of x minus one we multiply by The accompanying facility of this is the square root of x plus One but math is not allowed to multiply in the denominator You just have to multiply by the numerator, which is the square root of x. Plus one a minus b in a plus b above The remaining is the square root of x plus one, and the denominator is The first square root of x A quarter, I said the square root of x, so the square is Sh He insists on going to the first X-square minus square The second one, yes, and this is my opinion if we focus Same as GLI XI, right? It means you can see from far away. Audi says the phrases are not equal to the countries equal but this phrase is equal to the phrase The definition set of the function AF is The function g is equal to us And from him, it is equal to us, and bravo to the one who said it And he answered correctly, we come now to The example that follows The example that follows that is The fifth example has a kind of focus first. We go to appoint the DF definition group where We need x minus one times x plus one It is not equal to zero, Professor Maqam always differs About zero now a times pi does not equal zero It means x minus one does not equal zero. x plus one does not equal Zero is either not equal to zero or not equal to zero. It equals zero, right? This must not equal zero. This equals zero. Follow me now. Okay? This is not possible for it to be equal to zero, and this is not It equals zero. The important thing is that one of them is correct or it becomes If x does not equal one or x does not equal Minus one means that I have DF children Equal to equal to me except for the missing one A thousand greetings to everyone who is with me. Look. The identification group is the one who executes The denominator here is one and here minus one Let's go now to Digi if the definition group of the function F We found it, let's go now To Digi where what where x squared minus one Not equal to zero means x squared Ndi this is from This is a quote from Subh x squared does not equal one x does not equal one or x does not equal Minus and Ham definition set of the function G also is the R Mad one and minus one Okay, we understand this. If we find something that suits us, DF equals Digi and equals R what is missing one And one is done Now let's move on to the phrases: are they equal or not? Right, let's come to the phrase, or let's come and say who Yes, every X from DF we go to find NF This can be written as follows, if you pay attention: Mia, focus, I love you Focus on the famous identical opinion number one x plus where all square x plus where Everyone is square and whoever doesn't, don't post again. Square The first plus twice the product which is 4x plus The second square on this Ra is identical to the month The sum of x minus one and x plus one is The first square I said the first square minus the square The second one is x plus two, all squared. On x squared minus one and this is the same G for X, I swear to God, that's right, I mean the definition group We say equal and the same phrases are equal And from it If you are equal to us, bravo, let's go Boys to the sixth case, we will see you, we will see Clever ones, try it and you will see I have the sixth case. First, we go to the group. The definition is that it is a DF such that the denominator is not equal to Zero with us becomes LD equals AR what? Three, this is our morning. What three, that's it. Now we go to Digi Digi how how that The denominator is x minus three squared Every expression has a power of zero equal to zero. This power will go away, it will have no meaning If there was a force of 2024, we would transfer this and it would become mine. X is not equal to three, so what? Three R Mad Wash Three what does it mean professor It means that their definition set is equal. Okay, we understand this and write it. Here we say this If we are equal, DJ and Ray are equal What are the three sitting positions? We will make up the phrases to get to you For the phrase “th”, we unify its denominator and say: For every X-Mendy we have NF-Lax Equal to Arha Nahad Maqam this in Subhi X This is in the negative three plus twenty over x You need three, how much do you want to give us? You will give me this here. X this with gives me Minus one, this is the function expression. Let's go to the expression. The function Come on, let's see if the expression for the function is: The same phrase as the function. If it is true, first of all. We have no problem with the place. We will go there. The expression is x squared minus four x Plus three here boys focus let's go calculate The distinctive means we will conduct an analysis for it The special one is the square B which is square 16 Minus 4 times one times three gives us how many 16 Minus 12 4, my root of Dalat is left with me But don't worry, the root of "dalat" is "ar'a" which means two. We became x1 equals us minus pi minus the square root Delta over two here becomes one Two over two is one x two equals minus pi plus the square root of dt over two Become more important to us Wait, wait, wait, we will see something The last example means this is the simplest which is x squared minus 4x plus 3 factorization is Identity in the first year if it was a phrase for her Jan or equation solution we say a times x minus x And if X is minus X, that means Sobhi is minus X And there is an X minus The expression for the simplest is what it is written as. The phrase is "What will happen?" We say to her: Yes, every X is mine Inks, we have a written morning. Write and see if you can put this. We became x squared minus a x, excuse me, excuse me Excuse me, we write this in the parsed phrase. Allow me to do this. Here, give me X minus and X minus times On x minus three all squared a no It is permissible to change the expression of the function unless it is About us, the definition group is available. We said it. The definition set is AR except for the three cm I have the right to remove one from my side and one from my side Gilax equals us x minus one over x Minus three and these are my children, Ray is worth us, FLEX A thousand greetings to whoever brought it, I hope he is my son My daughter, let's stay in the comments, okay? See with me. I got out of DF, we are equal to Digi and F Lax. We are equal, we say that's it, but there is a bit of it Service but a thousand greetings to both my son and daughter We tell those who have tried it And from him, if we are equal, he brought it right, my friend Hailey's comment is not correct, leave a comment with nothing He said I tried, sir. So here is the first group. The definition of AR Mad three for each one of them I went The first phrase served the phrase the phrase Hers and the second one I abbreviated in it but it has to be Certain group definition may not be abbreviated The phrase only after specifying the definition group He is healthy now that we have finished the six cases We love you and you must understand all the subjects for everyone. Levels in the Akash Project Educational Nati now leads to something else I said The other thing is algebraic operations. I have two FF and G datasets known as DF and D G in order where Lunda and Ka are real numbers Follow me here, I'll take you to our operation. First, the sum of F means the god plus the number of the symbol Ours is F plus K Bq Mia is good for us as well Definition: We say this like this, I would Oh, that's it, plus K Lex equals FLax plus K where K is True constant, correct about us, the definition group as well This is what she becomes For example, we say “Uff” Lax here equals x squared plus one One did not affect the group that was this I know you even if you come here, Professor We said the root is positive. What is inside this root? Always positive, we have no problem if you come So there is no other word, but we said As a real number only this is the first case correct Now let's move on to the second case, which is: sum of functions We symbolize it with the symbol F plus G, which becomes L here. F plus G Lex equals us F Lux plus G Lax is a group Definition: The sum of two functions is the sum of the definitions. Theirs is the intersection of the two groups, meaning DF. junction DJ Professor Example: We said, we said, for example, what does Lax mean to us? x squared plus the square root of x = the sum of two functions square function plus square root function So we said this is an aff and we said this is a phrase Who came to us this morning? What will this group do to us? Her definition and what is this definition on the R This is her definition group. Focus with me. Zero plus infinity Zero plus infinity The end of the intersection of this group domain with this The field means So the first one is from us, ha ha ha, and the second one is from us and back So this is what my definition group will be Mine is zero plus infinity Two functions whose definition set is the intersection The first definition group with the second We want you to focus on this very well. We didn't know Here here I have here I have the quadratic function square root with We also broke this. For this example, we also go to the product. A function with a number that we denote like this: Wonda in F. We said that its writing is Lund of Lux Londa is equal to A A If the function is multiplied by a number, the number remains. The definition group always remains DF. Because this is a constant number, not a minus function. I have a constant root of x The symbol for the two functions is F, sorry, F times Here we write FVG LAX We are equal to F Lux hit G Lax Wash come back here and this is the same definition group The total scenario and the total outcome The definition of them is always DF intersection Digi example, for example, if we say what does Lax equal to us? X root X is with me nice X root X here Very good The first function, if this is the expression This is the second function, this is it Knowing that the meaning of the word is infinite Plus infinity intersection, excuse me, intersection, excuse me Definition set of the square root function It is from zero plus infinity to the intersection of The group's field is this field with This is equal to zero plus what no The end of the product of two functions is also a set Their definition is the intersection of my two groups. The definition is correct, so is my friend Here to the result Divide F by G the symbol is F by Y this The symbol is written F on G like this: LAX F-Lux equals G Lax, but the definition group is here Two conditions, the first condition is that We need the definition group to be DF intersection Digi with Lazmna G Lux boys are not worth it Zero is necessary If any two functions are together, we say the definition set. The first one intersects with the second one, since this We always said something must be present in the place It must differ from zero as in this example. What we talked about This here is a square root function with If there is a position, we say that this is the root of x minus One is not equal to zero. Listen to Mia, it's good. We assume this is the function. For example, we give this, we give this example, we like this They all come out understanding, for example, Dina has a root of X. Plus one over x for example minus one So here is the function of the expression of the god F and the expression God is here, if we say this What do we have to do? We have to do X so that X Plus one is positive and x minus one is not. Equal to zero, we understand the word, professor. It means it. The intersection requires that what is inside the root be positive. This is amazing Alone and what is in the denominator is different from zero Become equal to me x so that this is k nq become me x is greater than or equal to us minus one and transfer this Who becomes my X is not equal to us One Kong we make here the base of the fields where Zero for example We have from us from minus one plus infinity We said here minus one plus infinity, that means So the spirit with X does not equal us one means Here One said this to me and this is not a group Definition: We said the intersection of the two colors, good morning I wish we were equal to each other, or to one less than us For the open one, the union of the plus one is what Infinitely this is the definition of a set of phrases I will repeat this type of thing over and over again. The definition of a set always breaks. The two groups plus the denominator is not equal to zero This is a rule we read in the first year. Because we must understand the values Forbidden after we finished my children from the element The second one is that it is equal to two functions. We will go A very important element, but it needs focus. It is the composition of functions. I do not advise you to do anything other than that. In this second edition, there is a detailed lesson. Plus several practical exercises, all of which have their own uses. Their titles are on YouTube, but we love my son and daughter. Come with a notebook and pen and we will continue with the definition Focus with me on the definition, then we will do a practical exercise. You will graduate with understanding, God willing. He said, “Definition of ‘Uff’” And G Dalt is not known on DF and DJ on The order means DF is the definition set DF And the DJ said that for each issue Real X from DF that DF LAX belongs to Digi, focus, focus, don't worry, understand what we're doing The examples are very clear. He said the function is composed of... Followed by the function c is the function that we denote It has the symbol GRO-AF and reads in Arabic FF is a G structure, meaning that FF is in the belly of G And knowledge on DF where GFX GFX We call this one a daughter and we call this one a mother The girl is always in the belly Mother is an example. Notice in the examples that he said, “If it indicates something.” Knowledge of the domain of one plus where AF Lax equals us root see with me well AF The square root of x minus one equals Let's look at this function, AF, AF. This is a compound function. For two functions in Where is my love? This and Alfie are This is the ALAX. Our expression is X minus One or The fi is the root of X with us. This one is in the belly of this one. In the morning, we say that AF is a compound of two functions. Any structure where the expression x minus one And the thousand is the root of x. An important note. A note in The general case is that the installation is not a process. Its meaning is J F, not EQ Y Generally, the composition is not a process of exchange exercises. Apply to all of the following: Eye group definition Afji and JF then Ain phrase Afji and JF or We say GI is the composition of F, and here F is the composition of Y, come on. Now we have five examples that are going to graduate. God willing, you understand the definition very well. True in every case The solution The solution here is to start with the first example which is He is AF Lux, how much are you worth to us? You are worth seven to us. X and GX equal X plus 20, right? We love you, focus with us ponds This DF is equal to AR, this is a linear function. The function is also damaged Come on, let's do it in front of you, right? Let's come now to... The definition that I mentioned here, look with me here. If Rungi equals Ha Look, the rule says X. So X belongs to this is the daughter and this is the mother This one we call the daughter and this one we call the mother We start with girl X who belongs to DF, sorry Digi And Gilax belongs to D Oh, nudity is not something that can be heard without reason. We have become We equal X so X belongs to DG R and GX, these are not with me This is x plus two that belongs to D. FDF here how much does this DF belong to I came back, professor, and I understood the example. First, what does the rule say? DGX where X belongs to YG and GX this In spirit it belongs to GX it belongs to D The first girl's introduction group for the girl The girl is not what her phrase is Belongs to the definition group Mother teaches complete examples. Increase them. Support if here I have RAX belongs to A Wax plus two whatever this x belongs to If this value is achieved directly, it becomes my DD. Please make us equal, I don't understand, sir Look, no matter what X we bring, we put it here. This is an X, we put it here, whatever it is, any X, and we add Two remains this value always belongs to AR The definition group is aware that I have noticed some The students tell you the professor is the intersection of fields No, the intersection is not necessary in the first place We understand the speech, it is not given, it is not given, this is correct Let's go now, let's take the ferry out Of mine If Rongi X is worth what did we say this is a belly We become equal, oh sorry, oh LG X, see with me, F, Rongi, Lex, we are equal to F LG Lux means you become equal to us, let's go get it The expression for the function is: What is the function? In each x, replace the function y with gD. X in every X with us, morning seven in G Lux Professor, I did not understand. Why should we put this here? We put it here, what does it equal? ​​It equals us. This is the answer. Put it here and you will be in X plus. Two is equal to us x plus 14 Who is this, AF? Jax, this is the only one we're going to do now The reverse of DGF equals the same base x So X belongs to you, this is the girl it belongs to To DF and FDX belong DigiX belongs to the definition group of The girl and the girl belong to a group The definition of mother is as the rule says according to Definition: Good morning, we have good morning, we have good morning, DGF X equals us So X belongs to DF, so DF belongs to our X AR and FLAX belong to Wayne Ray FX Tai Where is the seven X that belongs to R? because Digi Shin He He Ar and this talk whatever it is Any X we bring and put it here, the value will be achieved If you become my de generosity, I will be equal to you Ar health, come now to the appointment of the phrase A G R If Lax is equal to us, GF Lax is equal to us, let's go For my function g, in each x of it we substitute BF LYX becomes LYF LAX plus two Go to X, every X of the function is G, replace F Lax in the morning, what did you bring this value for? Put it here, it becomes seven x plus two This is Genero F Lux. Let's go see the operation. Change it. Look what she gave us. Seven X's plus. 14 And here she gave me seven x plus two is called With what, with what? no Equals what I said note [music] Correct example, we love a leader and he must complete it Watch the full video to get a full understanding. Cases that are not allowed to go out Complex definition set Let's go to this example as well, which is DF Wa. equals us Hanadi Al-Maqam Mama told us about the group We said the denominator is always different from zero, good morning What's missing? Let's go to Digi now. The function has no roots or fractions. The group gathered around us and understood Now let's start the introduction group. This Come on, let's make X equal to X, so that X belongs to Digi and GX belong to DF this girl This mother is always the daughter and the daughter is The definition group of its content belongs to The definition of mother group, this is how we became X is equal to us, such that X belongs to DigiR. And G-Lux huh G-X which is four X Square minus three x Oh, we love you here. Focus. I have to say that this is what GLX is for. The value belongs to this group which means This we focus again, this is what we click on x is not equal to Minus one means you realized that We make this equal to minus one, and we like this Focus on GLX belongs to DFG I have this with me We put it This is all, this is it, this is the mother, this is the thousand She is the mother, so bring her, put her there and say, "This is it." Lax is not equal to minus one, this is what we love Focus on it, right? It became X, so X belongs. to ar and four x squared minus three x We return this from plus one not equal to zero Professor, do not return to the definition group of the function G is AR where G Lax is which is this It belongs to this definition group and it differs from What about one? We bring this to you and say, "You..." We must disagree on the minus one, and we will return this from us We will see, this is guaranteed, Ark will remain We go and calculate it as special because it is a degree The second feature is T Minus 4 times 4 times 1 gives us 9 minus 16, which is minus seven, is exactly less than zero. Oh, what is this phrase? No, this phrase is not acceptable. The solutions to this equation have no meaning, whatever it may be. X, listen to Mia, it's good, whatever X is It belongs to any value we put from here, whatever it is. This value remains initially equal to zero, no matter what. X was a word, whatever X means, I like it We graduated this profile group Come on, my kids, join us Oh, sir, I did not understand. Bring any number of us. Here you hit achieve what is impossible equal to zero Impossible equals FR, meaning all numbers are true And we realize that the phrase is correct. Graduation definition Ar AFX equals AF For x and x of the function, we substitute Come on, you're one on YX plus one I don't understand [music] This is the jump, we became FGX, we became equal to one On X-square, sorry Four minus Three x plus One ji jeebua ji ha jeeb Put it here, let's go see where the place is We forget that it does not disappear as long as it does not disappear, no matter what X was with the definition set is the one who understood This example says Morocco understood the whole This is the first case, we are now going to The second case is over. Now let's go to... The second case So, as long as the phrase is understood correctly, the group The definition is correct, but the sentence is incorrect. This is where the phrase "It is forbidden" comes from. Serve it in the draft For the record, Anon is now escaping to DGER F X is equal to us, so X belongs to this girl F and F Lux belong to Digi we became like this X So see Mia Malhih X belongs to DF with X belongs to Rmad minus one and FY X which is one over X plus one ha f Y X Belong to ha to digi to ar Oh, the clever ones, see this. Do you understand? A group came out. Come on, let's see with you, X belongs to DF X-Ra belongs to R except minus One waffle lox which is this one belongs to Are what the definition group becomes me DGF I want you to see with me what this value is. Meaning if the position is different from what about Minus one, this minus one becomes a group The definition of Audi is R-Max minus one, that means This is one over x plus one then Meaning and why x is different from what minus One ha x belongs to r mada minus one My profile group is this, let's see Let's get the phrase out. My words are true. GF Lax becomes LI equal to GF Lax And it becomes equal to us, come here to All become mine, become mine four in F-lux all A square minus three in the x says we go For the function G in every x we ​​substitute Bash in thousands Good morning, AF Lux Square, and here, AF Lux, look at this We are equal to one over x plus One squared minus three times one over x plus One here if we start to see don't worry about this I mean, I'm missing one, and this is about where I'm missing one What is missing one and what is missing one? This is the AR G Afx Al-Fathiya, this is the correct definition group The phrase is: What is the difference between AR and MADA? Bravo, we are now progressing. We are done. This is how we love you. I started following you with me. We understand that we love you completely. Be patient with me. Be patient with me. Now let's go to the example Thirdly, it is DF Ra equal to our star Professor, the position is different from zero DJ I see a corrupted function May you be blessed or may you be blessed X So X belongs to DG and GLAX belongs to To DF we read in the definition Only a girl or always here a girl and a girl We have become equal to x, so x belongs to to This is what this is. Look with me at this. X minus One belongs to DFDF who is she? Ar star word translate with x it is no It equals zero with us. We put this here. Put it here so it doesn't equal zero. That's it. Empowerment Show XR Star with us X Naha No It equals zero. We bring this to the square root and put it there, so it becomes x. Minus one is not equal to zero, we become equal to us X so that X belongs to AR and return this and X Different from One, we are back Good morning Come on, let's do it together How many times does one walk before we can take the ferry out and see? What Oh my God [music] Xana Lgx is with us in every Xtaa The function is to compensate by coming to me one morning On Gilax plus five we are equal to one On the edge of the pocket, this phrase is like this, we put it here We went x minus one plus five, I saw a group The denominator definition is different from zero with x minus one does not equal zero x does not equal one Here, Umm Ali, one We got the right words 100 Right, we go to the club to do the opposite like that The opposite [music] he Effx so that X belongs to D AFX belongs to Y Correct, the same rule applies. Correct X so that X belongs. to [music] Argh waf lax which is one plus x Five What do you belong to? Ar This is what belongs to this now. This is what belongs to this now. Always true if x is not equal to zero cm Good morning Yes yes G Ro FXO gives the final result directly If any number can achieve this except Who is the zero with us? Good morning 1x plus 5 then it is M with A real number if x does not lead to zero Morning assembly Right because it doesn't have to be zero, but GF Lux We became equal to each other, I love Lux and you become us We are equal to each other Here in every X dough we replace with BAF it becomes mine So FX minus one means you have to subtract here Thousands and thousands here we become equal to one on x plus five minus one equals one over X plus four tell me what is the set of The situation Star can even contradict that I apply in the definition correct 100% for this, I noticed that this lesson is very important. Even some people on YouTube are explaining it. But there are some errors that we do not need to appreciate. We mention the people No, but we always recommend that you do not give away knowledge. At every sh They are explainers, but the method is explained differently. From the chaos, that's why I warned you. We tell you, I am not good or anything, God willing How much do you understand? We just explain. Now we go to Example The fourth is also the fourth example which is Naj to DF if R in the fourth example Ra equals us AR and DD are equal to zero, sir Why do we understand that you only write that this machine is not There is no break or root in it, and this is the root and the root What's inside is what's inside Now we come to DF Runge equals X so X belongs to D G and G Lux belong to DF, we became X So x belongs to the domain of zero plus what No end, look with me well and come to me This root x belongs to Focus Good, we said X belongs to DJ, which means X is mine It belongs to him and G-League X, which is this. She belongs to him, she always says this It remains verified if this statement is x root x Always belong to AR when If the number here is always positive, it means Good morning Ongi equals us from the field from zero to Zaad What do you say, Professor Nadir, the intersection of the union and the intersection? The Union must understand what is meant by this talk If my X was the first one to come, I will come Here, x was positive, so the square root of x was always An important real number. Now we go to F. X equals us F LG Lux and let's go For the function f in every place, we substitute in c Good morning That's how it came Lax, excuse me, Gilax squared like this plus two times Jax Plus one becomes x, which is the square root of x. It becomes the square root of x, which is x plus Two times the square root of x plus one, sir. I did not understand. Bring me this root and put it here and a quarter of it is a root. x squared is x plus two put a root here x becomes the square root of x plus one Here is FGF circle GLX GF Runge Lax is correct, this is a definition of zero plus because this is a This gives us this plus zero. Correct, correct, the group now looks at the matter The opposite, but we love you to focus with me and see The reverse order is clever DDGF equals x such that x belongs to To DF and DF LAX belong to Digi become About us X so that X belongs to Are and what is this? I want you to focus with me a little bit Which is x squared plus two x plus One to be Positive Professor, this is originally ours. This is its exaggeration. positive It is positive, meaning that when we say that Afex belongs I have Opposite this, this, bring it and put it here, X square plus x plus 1 must be positive I understand, this is X. It belongs to me. Put it in my pocket. Here the word belongs from zero with the meaning that it is positive This becomes our X such that X belongs to Ar and this is originally Ray X square, sorry X Plus one squared like this, right? I see Shawn telling me what this group is Jeff X belongs to the R whatever X belongs to We put it here and the value will be positive no matter what. Whatever the word is If you want, we should go out on the ferry and see Is the group graduating from AR or GFX? GF Lux is worth it to us We will bring this god This is here like this, square root of x plus where x is. Plus one which is equal to the square root of x plus One square and we know the lesson of Tyrannical x square Under the root comes out the absolute value of x as well The absolute right hand comes out as Lax plus one. The value is the same as this and this is a shelf on the ground floor It has a root The station of Arafah is known to all, a thousand thousand thousand times Greetings to my sons and daughters They follow Accuracy Good health, let's continue The fifth example is with us, God willing. We have a full point Fifthly Avoy R and DJ One, sir. We understand from one, not from inside. root We read this We read it together Add this to understand or read it X bigger or equals us One by one, x is greater than or equal to one. Focus. With me because we need it later, right? Let's start now. To this Come on, let's make X equal to Digi. WG Lax belongs to D If it becomes so that XX belongs to Digi It means that it belongs to one person and its end is greater than its end. Couscous is the root of x minus one. What is it? They stayed with me and G-Lex belongs to DF Meaning This is due to the Balq X belongs to Digi KM Z Nhaya Ho G Lex here I come X belongs to R Whatever the number that comes from one plus one, we put it Here he will give What does he give us? Audi gives us a verified value. Bring any correct number. So if we put it here, we get x 5 minus rb Correct, any number in the domain that we put here is one of ours. This is my graduation Come and make us equal One, this is what is meant. Let us see what number we need here. We put here the value achieved with us, the picture is the same Okay, let's come now FGX equals us FLGX equals us I survive every phrase from The function F is replaced by G, so it becomes L2 in G. x squared plus one equals two g lx And behind is the square root of x minus one squared plus one The square root is equal to a quarter of what is added to it. Two times x minus one plus one becomes How much does it cost us to have two X's like this Audi Focus with me, don't mix things up with us in Aqaba We complete this morning, this is it, and this is it, minus two Plus one becomes equal to two x One less, here is the phrase, which is F Rongi Lax we said this is a root cause you become X Minus one we publish this two x minus two Plus one gives us two x minus one Correct, sir. We understood something about this statement. Knowing about you and the definition group I got you out of here Even if this talk is too much, it is necessary Get to know the definition group And I have all the subjects for all levels in Akash Project Educational here because we have to understand something For example, let us give you an example. Is this phrase like "Af Lax" equal to us? two x plus one over two x plus one Is this worth us? one two x plus one over two x Plus one is equal to us One can not say equals one except If we say that two x plus one is no Equal to zero, we transfer this from zero, so we have two. X does not equal minus one with us X does not Equals minus one over two, we say F Lux We equal two x plus one over two X plus Z equals one If x is not equal to us minus one, where? If x equals minus one On the morning we have a number on zero and this is originally Not acceptable in Mathematics is why we recommend even if the phrase came out You have it like this, but this phrase is true unless If it is her field There is this phrase that we cannot say that it is We are equal to one unless we say x does not equal us Minus one, where or is it not permissible? We don't tell him to pray unless he is in a state of ritual purity. Human or complete conditions if these are the twist I said here, be careful with what you say, but in the original It's not her, it's her, why? Because we come to apply it. The definition itself and this example are in The book is solved, this is it, this is it, right? The definition set is zero, so make it easy. I made it so the exercise would be more enjoyable. Now let's go to the example that And also the example we said here is Bi Rana We mean X is greater than or equal to one now Gyro FDGF equals us access so that X Belongs to DF and FX Belongs to Digi becomes us X so X belongs to R and If Lax is two x squared plus one One is greater than or equal to us, professor. I did not understand this. Afx Bring this. I told you to put it here for me. Two x plus one to put here is It must be greater than or equal to one Let x be ours so that x belongs to r and This is from and this is from under two x square is greater or Equal to what? Zero is x, the sum of any number, put it here and a quarter of it It remains positive, so DGF equals W Ar equals A, which means any number we take out of it and put it Here remains the investigator of the group, T Now Ger Ar In X, we equal GFLAX and go to the function In each x, we replace it with the function F, and it becomes equal The root of the function G is: Here we replace F Lax. One less and we will see our graduation and good morning The square root of f is equal to 2x squared minus One, excuse me, plus one. We put this here with... One less, sir. This is a pocket Put it with me Good morning, we said that the root of x is equal to The square is the absolute value of x. We have this. The square root of ethene times the square root of x equals the square root of two Sorry, in the absolute value of X, it is not worth it. Divorced, look in front of you, this is the number of this Number of absolute values ​​on the identifier on Oh, bravo, here we have given these examples of love and my love I understand well, leave my comment, I understand how to get out The definition of a compound function is a function. The product of the complex of two functions by definition We are still figuring out how to do it, that is, the direction. Change and I said I explained here Exercises mean in one way it is fantastic Install special functions for the version in everything you need We are re-issuing a new version of this version. For example, who talks about the structures and representations? The lesson plan is very good after passing Tests, for example, test number 3 Number five test Number six test Number seven And the assumptions mean the test number is valuable. Look at it. Here, I mean, tests don't say you are full Test No. 11 is important. This version is recommended. He is in good condition, thank God A very large book, imagine how many there are. It has 377 pages. Double glazed effect, there are nearly 800 Big bag means very huge, so we recommend it Buy it now and you will find it in the store For the first time in Algeria, the book that will happen Difference in your study of mathematics in the year Second secondary book explained in detail page In the easiest way for free on the professor’s channel Nour El Din, the second edition of the book series Silver All you need in one book Study With all comfort and confidence, be one of the best in everything. The states of Algeria prepared by Professor Nour Religion in cooperation with Akasha team, request it from The library near you, Akasha Library, more than Just a publishing house with Akasha books, the joy is complete After the baccalaureate, my children will go to the next direction. The functions have changed, but we want you to be more patient. With me, where we recommend this book to you The second one is the direction of change, especially the composition. We have explained the functions in a very boring and long detail. Mia's exercises, my daughter, my son said, direction The function changes from θ to θ, which is the θ theorem. A completely monotonous function of the field of what we hear The word completely monotonous means completely increasing or Exactly decreasing as a real number for the function of the fig FF plus KA same direction of change on The field, notice the examples so you understand, my children. AF is a numerical function defined on the domain from zero Plus m infinity where x squared plus a This is the k This is here it has the same direction change The function A square on any increasing domain of Zero is not with me the square function. Do you know what zero is? Zgi is looking up, and the function is refined. This is the phrase. x squared is also completely increasing. This means that the number that did not affect the direction of change The function This is now the direction of change of the color function. Yes, I have a good theorem that you follow. This is Linda is a real number that is not zero. Totally monotonous on the field ie always say why We say monotonous, completely increasing, or decreasing. Ok, one is a real number, not zero. Listen. The first case is if Londa is a positive number. Five Three, four, the important thing is for the letter D, the letter T, and the letter F The color of the AF is the same direction of change on the polisher, for example. For example, I have five if if This function was increasing on the domain, i.e. 5VF is also increasing in that field. If the Londa is negative, the direction of change will be How are the functions F and Linda F inverse? For example, this is increasing, this is decreasing, for example, AF Minus five F minus five F means if This was a friendly auction, so know that this is… Decreasing, but if this is decreasing, then know that This is increasing, meaning this is Londa's influence. In his reference, if it was negative, it would affect the other. It was positive that it affected the direction. Change, if this is as we said, we said, oh, Linda We are in conflict over the field here, example example The function 5x squared is increasing with The domain is from zero plus m to infinity like the function Square and the function minus five x squared is strictly decreasing on the range from zero plus Why is the function squared from zero more than we said? The number is increasing and this is the number we multiply by. Negative if the value becomes decreasing we go now Thirdly, the direction of change of the function JF or F Installing J is one of the most difficult things we love. My sons and daughters focused on it and the release Second, this is Rani for you here, the exercise in Page 24 contains 12 examples of function composition. Explained in detail, for example, its address on YouTube This is a detailed and accurate explanation of the functions structure of the Sunnah. Second secondary school, Mr. Nour El-Din This video in particular gives you health. Listen to it. I have a good one and we will solve the practical exercise You will graduate with understanding, God willing. He said, "Proof of what happened." A completely monotonic function on the domain of any monotonic word Totally increasing or completely decreasing Function rank exactly on Field, see Mia, thousands of ranks there on the field Her salary is exactly what she deserves in this field. Its where any content in C means this The field is about the image of the content in The field is a little bit different for me if it is for Two functions, F and G, change in the same direction. The function GF is strictly increasing on any domain. But I noticed a lot here until he collected it in YouTube They explain here what I think, and this is not the extra [ __ ], I don't have any more fans, if it was like this Increasingly in the field of its growing AG Its field is G where there is no content in G The function GF is increasing on the domain i.e. This one heard Mia well, but if it was Change direction The function F and G are opposite, meaning one is increasing. In her field, yes, and the other is decreasing in Its domain is C, so the function is GROF. Completely decreasing on the field Yes, we must not waste time on this topic. Practical examples, practical exercise between each If the function F is a composite of two functions, it is required Determine their direction of change and deduce the direction of change of the function EF. Follow me carefully, my children, how will it go? Explain this point Exactly, if we follow closely, if Ben tells us Notice that the function f is a component of the function t It is good to start with the first example. If we start to see here, my children, there is a sign If we look at the square root of the function, we notice that The solution: Pay close attention to my opinion. It is in a circle. This is what we call the girl learning and this is what we call The mother is like the daughter in the mother's womb. Notice with me. Nice, where and where is this function of mine? Our phrase is X minus one The function in my children is what it is, it is x squared so that If you bring this, put it here and put it here, it will go away. Get the function F and let's try it In front of you, AF-LAX, you are equal to us in the A-LAX circle It is equal to us in Lao Lax and it is equal to us in Wayne I mean, come on, look with me, where is the phrase? I wish they would give it to her and put it here, which is where it should be. X minus one after the function in here where Look at Mia, I'm going to your house, my son and my daughter are here X minus one, put it for him and put it for him, what's the morning? Our equation becomes x minus one squared and it is The function f cm is true that the function f is complex There are two simple functions that are a null function Followed by an auxiliary I hope you understand the idea well. Good, good, good, give us an example, professor, before what? We go to this, or we go to the AF LAX function, for example. For example, it is equal to cos x minus 1. This is also the case. The function: Let us see the composite of two functions, the alphabetical function Which is x minus one and the function is cos huh Where is this, my children? This is an X minus One and in Lux which is Cos X so this When we put it here, it becomes cos x minus one. Which is the function of F and Druk, we will see if This is the first point that is necessary We know it as the function of F. This is true. A composite of two functions, a distorted function followed by the function square True, but he has already confirmed that we have the function of F It is a compound of two functions, i.e. a compound in or in Circle, what health now? If we come to the police station, he told me And conclude the direction of change of the function AF we are going We serve in this match here who love my children My daughters should focus on me first. I need to know. The direction of change of the function is the function Follow the box here with me. We will explain now. in detail Here we come now to the millennium function The direction of its change if this is its direction Positive, then my function is strictly increasing. But if my null is negative, then the function The millennium is completely decreasing this first We go to the square function. The square function is not known. It comes increasingly Then decreasing then increasing, that is, the curve He takes us out, this is how you learn everything, huh? For me where here I have zero so the function is squared from minus infinity to zero decreasing from zero Plus infinity increasing function reciprocal of what You know, there is no knowledge at all, at zero it is called You come to us diminished from us and you come to us incomplete from us So this function is inverted, but the function is The square root is also a function from zero to Excess of being Increasing if the millennium function is good Let's see if this is positive Increasing if this is negative Decreasing function Square from minus infinity to zero decreasing from Zero is increasing, the function is the reciprocal of minus. Zero infinity is dead From zero plus infinity to decreasing infinity The square root is also from zero. Plus infinity we said zero plus what No end how it is completely increasing huh right this We need them because if we don't know them, they won't be able to help us. We solve this exercise on composing functions if Now let's come and start something right if we say this If we see that it is good, the function is broken Followed by a square root, if we come to this point We are talking about the direction of change if we come to this as well A distorted function followed by a true reciprocal function Professor, that means This is this, F-Lux or F-Excuse me, we say F-Lux She is equal to us circle where Where are you, excuse me? It is x minus one, but the L is one over X so that when we bring this we put this here The second case The third case Also, AFRA is also a compound for Two circles Where is the damaged function x minus 1 The function in is the root function The square is the same plan here as well. Circle where the phrase is about us, it is the same Minus x, but our expression is 3 Minus the root x so you understand correctly my son and daughter T Bring this and put it here. Your function will work by itself. Here it is Now, answer our first question. Show in each case that the function f is a composite. Dalton's first example is a function that we said is corrupted Followed by a square function followed by a corrupted function Reciprocal function A defective function followed by a function The square root of a function is followed by a derivative. square root function Same plan now, we go and this is how we study The direction of change so that the speech remains applicable in this I have said many of the proofs, even in YouTube as a group explains it in a different way Clearly we follow Well now you know what we should start serving first. The definition set of the function AF is AF. Give us the answer first, so we can go to This is the corrupted function that is defined on R And also about us, since the function is square as well The definition of RR here in my example is I know where the hell it is. What do we need here? We find the direction of change of the function F in a way True, but we want you to listen, my son and daughter. Make a schedule. Change this and make a table of changes for this And you will see how he noticed the idea with me. Notice this. This is the simplest idea we are trying to explain with X and Hanaya. Any lax minus infinity plus no This is the end of my function, if the other one is Its positive is increasing and we are looking for it where It is missing and we search for it and where it is missing we do this x minus one equals zero in the draft My morning, X equals how much? One equals this and that. Come back, teacher, we'll go first For this function, we have a table of changes. We'll go and look for her and see where she disappears. Also for the mother function, where is the opinion of the mother function? Which is this here I have what I have X of Minus infinity plus infinity And I have it here in LAX Here is her change schedule, it will come out like this Then this is zero. What is the image of zero? Don't worry. Swap here with zero and you will get zero. Well done. Let's do this. Service here we can serve in my charity 100% correct. First, we make a change schedule. This and we add the change table of this and we start working In front of you now see the charity that I lost We apply it exactly, right? This is how it is from us to us Yes, I died Extra Exactly on the field from minus infinity to One look, I recommend this, this is good, this is here field If we see what is missing from one, what is the field? The value of this field's image is this. Which is from us to the bottom, this is what we recommend to you, this is it The field that they are talking about is Darkness For the field This is what you see in it, it is missing the end For one of the pictures as well, where is it from? From zero huh and zero in front of you huh zero cm this This is the same guy. You can see what's going on. The police insist that you see what we say Look at the field, it is missing something, it has no end For one picture of him, he is missing something infinite. Zero, which is what is missing? Zero this is my friend this is the domain C function My mother is from minus to infinity to zero We say and believe decreasing Exactly on the field of minus zero. Yes, look. Mia if the two functions F and C are in the same direction The change if the direction of change of the two functions is F And the opposite side is true for us in the second case, how? This girl is increasing from minus to one This is the picture of the one who is minus from zero Here is the bidding, this is from minus to zero, decreasing by one. From the most to the most decreasing, we say, and from it, uf decreasing Exactly on the field, going from minus to zero, no He says he is in the field, that is, here is the field On the range from minus infinity to one We always go back to the origin, which is Okay, let's go back and see if you understand the first example. Let's solve it. Installation problem first we said the function F A composite of two functions, a distorted function followed by a function First of all, we go to create a table of changes. The daughter function and we make a table of the function's transformation Mother and we will not see from this The given data is correct. We come to the domain here since the function is This is mine, professor. I have not worked for anything. The limit plus m directly indicates that this function is not Totally monotonous, listen up. It's very nice, if only I had come from a camel here. My function is going up and down, it is forbidden We apply the charity wrongly, if we apply it we must give Where is the monotony, I mean one is going directly One is going down to the direct and no one is going to the direct A [ __ ] going straight up or a [ __ ] going down straight down I'm going down the drain directly, but we don't see each other It tells you one is increasing from minus infinity Plus infinity and another says from its end what You don't miss out, you don't miss out at all Other than this part or this part, this is it The charity is here, where the mistake is made. We should say this. The first case is that we say, “What is the result of the part?” The second one Increasing Exactly on the domain of one plus what not The end of the realization of my field The second one, huh, Wendy, this is the picture of her Zero and we go out here from zero and here comes the field Mine is my field, so I can't find it Fiji content means the image is complete. Here we say And in Exactly increasing on the range of zero plus This is endless bidding, this is bidding, this is endless bidding Same direction of change as F Totally increasing, we always go back to this The field is completely increasing on the field completely On the field which is from one plus no Finally, a thousand greetings to every student who repeats the idea. Alone, if the first thing I thought of was installation, I woke up This function is a composite function. We will go. We run the first and second phrases, we go and run them The first and second changes table We start serving in the charity in front of his eyes, right? The first example, now we come to the second example With Akasha's books, the joy is complete and the average is high. And the ululations of the successful person will come, God willing, in his office Akasha is more than just a publishing house with Akasha Books His joy is complete Baccalaureate as well as the second example we said as well I always have an opinion in a circle, where if we see here How much is it worth? I want the RAX to be minus one, but the F She is one on X Hanaya, this is her AR, Ama DVD HERE STAR HA ONE ON X SO THAT I wish when we always bring this we put it here in its place This will give me the function immediately. Okay, let's do it. Now also the table of change is this x minus what not The end, I don't like it, I don't want to worry, and here's what Lax we said opinion like this where this phrase is absent We always look for it, where it disappears. It disappears when... One for you, then we will come and make a table as well The changes in the mother that I lack End plus infinity see here star Zero is a forbidden value. Here is the table. Let's go and say this is in Li X. We said it was decreasing. decreasing Decreasing, decreasing, the function is the reciprocal of the correct one. We put it here We start saying as well, so pay attention with me one thousand The function What is the function The function What is the level Here it is The domain of any function Increasing Exactly on my field who is the field Mine is infinitely imperfect One by one, here we leave it open like this, why? Open professor because what is one of them? Minus infinity for one open and from one To increase what is not The end of the day we study in the field of consciousness, we must rub I have this field and this field must come Open if my function is minus what is not The end of one is like a completely increasing circle towards I got this, huh? Where is it? Huh? We have zero We say from zero And in Completely decreasing on the field of minus Infinity zero open fan F see my This is an auction, this is a decreasing one, this is an auction in Its field is from minus one to infinity Which is the field of any huh? Rank completely and come This is decreasing. This is increasing in the field. Who is it? He is he from minus zero, what is the idea, right? Fan Af Completely diminished and completely increased over the field Mine is always from minus infinity to one Sorry, this is open, this is open, and this is open. We say the same thing again. Here is the field, let's say, how is it, it is too much? Exactly on my field which is from one To infinity plus and see with me from zero This field, these values, here, here, content, here, right? Here is the field where my morning comes in [music] Completely decreasing on the field from zero to Goal plus infinity, sir I said the function is increasing from a minus to a non-increasing limit plus infinity and the function in Decreasing T minus Z is not permissible because the value Forbidden Forbidden Health and completely inconsistent The field from zero to x. How is it? Increasing Decreasing Van F Completely decreasing on the range from one to Plus infinity This is a theorem that you must apply. In its entirety and to the composition you just mix Okay, okay, okay, we're done with her, that's it, alone Decreasing increase decrease gives us decreasing One decreasing bidder will give us another bid Diminishing means he did not say opposites. We are going now. To the third example and a thousand greetings to my children And my daughters who are here Follow and if you do not understand, leave me a comment. We understand that we will give you more examples about us thirdly as well If we start to see this, here is the function Who is this girl? Who is she? She is an X minus One and the function in is the square root function Oh, so this one equals us, R and D in Rahi We are equal to zero plus infinity Square root function of zero plus no End of health How how my children we do this XI LX We manage this so that all things come to you in a simple way. It is zero from zero. Now we get to the function in X And Fix, which is also known as zero plus nothing. There is no end and it comes around like this That's right Let's start here directly. My field is one. We will say, we will say, yes, how is it? It is completely increasing in our field. We tell you from minus one hundred to one, no, no, no, no, no One plus infinity because the set of One for the sake of what is the end, if we are from here, if any Exactly increasing on the domain of one plus what There is no end to this, it will not work for me From one to one plus one, that's it. The rose This is Wendy from here to us and in Exactly increasing on the basis of zero plus what Infinity Fan F Totally increasing on my field which is from One to plus What is this? Here is the photo auction. This is the auction. It's getting bigger and bigger Now let's go to the last example. The last one too He says installation if you see here with me a group of applications Who is missing the end of the boards? First, let's see if this is one minus X. If we pay close attention, it is 3 minus the square root of x. Professor, explain a little bit. Look, I want you to bring this. Give him a replacement. Look at this one. This is her compensation for him and her compensation for what I did not find This is the function that you find yourself in. Correct, correct, here. We also come to the definition group for this Yes yes it is R and D are zero plus infinity Have you thought of our introduction group? From zero plus zero Plus, we don't understand this. Let's start with a little bit. Change table and manage change table We will suffer and walk, we will suffer and suffer properly Ha x minus infinity plus infinity end Look, if it is negative, it will be Diminishing, look at what you think is going on This one is the same book, minus an X. Plus one, we see if it is negative. Where is it? Zero minus x plus one equals zero zero When one is compensated, you see compensation here with one less H plus one zero cm here one is like this We like this one. First thing we do is make a schedule of changes. And the phrase where is this missing? Let's come now to Change schedule The mother who is The thousand thousand we said from zero to plus, notice With me The square root function is increasing. This lesson is for the tribe that we mentioned, this is what changes. Look at the number multiplied here, it is negative since My function AF was the square root of Increasing and multiplied by a minus becomes decreasing It means you will come to me like this. You will learn this. Look. We love everything we explain with great precision. Increasing square root of zero plus m The end of what we multiplied by the minus becomes Declining health, let's start with some of my children We worry about what Where do we get our definition from? It is missing something. No end We say to one any decreasing Exactly on the field from minus infinity to One, this one, look at it carefully, this one, this one Anything that is less than one is decreasing, come to us This is from us here, it's the same This and in decreasing Right on the field of Zero plus infinity, here we go again, here is the field Mine is missing from one to one, from one to one with us Is this function decreasing? Look at this. The side they came down to becomes from us here as well One is decreasing and the other is decreasing itself The trend alone is decreasing and this is decreasing Van If decreasing Exactly on the field that is missing what is not Finally, a thousand greetings to every student. Let's comment on what I understand now. We will summarize the composition again. You must first see it. The second command vehicle determines the definition group. Each unit has the third command: Make a change schedule. Each one is a lifetime and then you start putting the charity It serves the unusable field. The function was completely monotonous, meaning it didn't match the example. The first one here is the square, it is not his salary, we have to divide it In two parts, from us and from us, but this is his salary completely But this is part of it, and this is a complete rank. There is a problem and I have to repeat it, my sons and daughters Here we give you the installation, especially in the version The second, I explained this structure in great detail. There are exercises in tests in everything Leave the comment with what you understood from Akasha's books The joy is complete and the highest rate comes and comes Congratulations to the successful one, God willing, Akasha Library More than just a publishing house, Akasha Books is complete. joy After the baccalaureate, my children come to the element The last important thing is the graphic representation. For functions, it sometimes gives me a drawing of a function. And he tells me to infer from it a drawing of a function, what is this? Which I first explained in the release. The second in the table is here, a table explained in detail. Here it is in front of you. Notice this and pay close attention. Let's explain it here in a table so you can understand, God willing. 10 out of 10 and this comes up in the tests It also comes in the baccalaureate questions. The last one said CF and CS represent two graphs. For the two functions F and C, respectively, that is, CF What is the function F and C? What is the function F? Teacher or EGY and number how is it real not Counted with consideration of the definition group of each The function F and the function Ash follow Mia, give me a good one It is good that sometimes a question comes to us and says to you, for example: Deduce the CS plot from the CF Rahin. We got up here on one table, we love my children My daughters follow well They try to fill in that table and memorize it. In it Inside we start now and I want to do the first case when Ash gives us lax equals AF lax plus Ka I mean, what is the shame of FLX? Notice the drawing of how we say the conclusion of SI Ash. Based on CF, note with me what CS is. CF image of the beam being withdrawn from his vehicle. It is zero, and you can see with us the examples, for example: It is the curve of the function F which is CF and give us Our function is written, what does x do to us? If you want to, I hope you don't notice The parts started to understand each other a little bit, for example. They give us here, they give us plus one, it becomes C for us What is the CF image with the withdrawal of the beam? In Sh Sh is the compound which is zero and the number which is Here is a guide for us on how the process is done. Here you go, zero one, here you go, zero one, here you go, zero one One, let's go to this blue curve and do it. By withdrawing from him, I mean he comes out and becomes ours Here you will learn this idea How does my curve become ha and where is that ray? Withdrawal This is the withdrawal beam in means This curve is in blue. I pulled him up. How much is one unit? This is number one if we say CS is a ray-trapped CF image. In Far and the number that they give us here means we run To the obstacle we pull it to the obstacle up this one we survive Now I want to For the second, when they give us what we deserve, LAX plus BB here inside, take note with me CS CF image with ray withdrawal. Look at it. I have minus B and zero in examples, all in examples Learn with me, notice with me what they gave us. Lux is equal to us, if Lux is equal to one, it is our morning CS CF image When his beam withdraws, see where it disappears. There is no one among us who is missing something Here, minus one, what do you want to bring back to us, one zero? Minus 1 is zero. If 1 is zero, how is that, professor? Here is the curve, CF, look at my children, we are dragging With one zero, that means from the plus jar, this is it The beam in and becomes my curve I see With me, it is good that this is the curve for me This is what we call CS. This is what we draw in red. It is SI. What is the curve? I ran it like this for a long time. Only one unit, this is number two, come on now To number Three, why do we have AX and FX? Plus, that means this This is a CFP image of the beam withdrawal. Why is this missing? And I was missing something, and here are some examples for you Professor Mama Kanna This is ELAX equals FLAX minus one Plus one morning we have a CS picture CF Balance that beam this where this one is nonexistent This is what one saw, it doesn't mean anything. Look with me. We always go back to this original curve. I will come We turn into one, and from us into one, that is, from us One by one, this is my result. The place is here, my friend. This is the Shafi. Al-Shaafi and come now We draw our curve. This is the curve. We drag one and there we go out with another, fall down here My children, look at one like this and one like that, come on My bottom line is here. She shouted This is number three, withdraw, withdraw, withdraw, gendarmerie We go to the fourth case, the fourth case is not We meet her, Yasser, but we turn away from her I would like to know what Lux is equal to for us in F-Lax Londa is an unaltered real number. What is the point here? One thing is a bit strange that we are hitting the arrangements Point CF in the number Londa to get CI What do you mean, Professor? Let me give you an example. We go to the square function. We go to the square function. When we come to draw a picture of one person, it is one person. The image of zero is zero, this is the image of two, and this Pair three four picture two is four So and so is the missing image, where is the four? Come on, let me show you what I mean, what we mean In this case, the curve of the function is a square. For example, he comes to us like this Focus on talking about this case. What does it give me? for example Our equality gives us one, for example, over two times F. Lax means the function F, we multiply it by a number S We multiply the order of the points CF by the number Londa, for example, we have zero. Focus with me. You will see what happened He insists, hit zero zero so we can hit him in the middle and he will stay Zero one, when we multiply by half, we get half. Look at it. With me here, focus with me, here is the X-square Substitute one for one when we multiply it by one On a one on a one I mean a picture of one One comes back to us, here is the missing picture Also, the one who is missing and incomplete, one comes back to me Also here after us is a picture of the quarter. Click to see. Monday's picture hit here where about us four They hit it in one on two, focus, focus These values ​​are always divided into two. Picture where is the picture two what is it Two pictures of two is two pictures of the missing Two is two, so look at the curve. What's going on? He insists, look at the curve, and he will insist, so you understand. Look at the puzzle The curve was like this, it increases and displays like this. For example, we said this number Your offspring are so ugly, you are equal to us in F-Lax What was this curve? Good morning to you, I mean good morning to you all So you want to see more of the pictures Here the pictures are small and here the pictures are bigger But the sin is negative first The whole curve is reflected because we talked about the function. When it is written like this, Londa F Lax we said if this is positive Londa remains Maintaining the trend of change that was this If we say that the direction of change is negative, then it will change. Auction becomes decreasing curve becomes aware becomes me This is how I want you to learn these ideas, despite this. We say it's not much, but it's programmed for you Now let's go to the case The fifth case, the fifth case, if you focus with me What are you doing to us? Minus the Afx, that means that this is not it But the color is equal to minus one, how is it? My London is missing one. Notice the C Ash Nazir. CF for the axis of separations is better We can't draw this, it was our religion Our teacher is a role model, but he is very stubborn I gave you a simple example so you can learn from it. I would like this for example Oh, that was it Ash ash lax we are equal to minus AF lax listen shsh He says CS is equivalent to CF in relation to the axis Commas mean the best speech is what says and indicates This is my curve So this is what CS looks like in CF. Axis of intervals This was That's right, now let's go to the sixth case, the opposite. What does Lax equal to us? If we minus X, look at the minus Here was Barak here I became healthy inside what do you say The base CS is the counterpart of CF with respect to the axis Arrangements means this is simple, memorize it once enough Haha, the curve, for example, goes like this One more thing, I need to know about the curve This is what he said, and what will happen to Nazir Saif? For the axis of arrangements, this part means See how his counterpart becomes him This and this is the counterpart part of This is how we draw our SI to be Here is C Ash Huh? This is it and the red are symmetrical with respect to This axis of arrangements is intended for one more example. Here, I want to explain everything to you. For example, my function is circled like this: Circle by circle This is how it is Here, notice with you the counterpart of the axis. Arrange how to become show [applause] This counterpart of his becomes Look with me and you will learn that I am always searching Let's make some examples, it's a bit difficult. This is how it becomes Look at this, I want to see This is the counterpart This is the counterpart Put your hands here and leave with this and that Opposite each other, this and that, opposite each other, this is it The counterpart to the axis of order is placed here. Who was who returned from and who was who returned this They learn The idea Okay, let's go to the case now. Seventh, what do you mean, minus, if, minus, X is missing outside and the missing is missing inside, this is easy Look at the CS vs CF comparison. The principle or meaning We know that you will see and we will see How, for example, do we love you? Focus with me on this curve, for example. this The curve, you see, my children, how it will be If we follow the process well, we will try to resolve this. Simple examples will not be complicated for you if we say CF this is what we said, what does LAX equal to us, minus FF For minus X, it is CS equivalent to CF. To the principle we were this is the CF here The principle is that we should go and look at everything This is for me, not for her, and this is the way I see it. No, look at it, as for it, or as for it to become This is ours Look at this counterpart to this one. And this is its counterpart. We can give a point. Another limit, this is its counterpart, this means The curve, for example, will come to us like this. Focus on your mind, here it comes What do you think of this red and blue? Symmetrical in relation to the Law of this appearance This is its counterpart. This is what we draw. This curve shows that CF and CS are symmetrical. Regarding the principle or Okay, let's go now to the example The eighth has a lot of tests, especially in Baccalaureate This question is always in the first place, for example. He tells you that the function is even, then conclude. Draw, notice with me what Lax is doing to us. For the absolute value of x I always said the question He tells you that I am married, so we say, "What do you want?" Look at him. Here with me Ken Two parts We know that the absolute value of x In mathematics, x equals us if Its x is positive and the absolute value of x is We are equal to minus x if its x is Negative cm here as well that the function is what this will be You write it in two phrases, either you write F Lux as you can This is what Lax did to us For the missing X, right, with respect to this definition group? No function is missing Very true Derek said CS applies to CF when X He is Positive and negative of CF with respect to the axis Arrangements for X to be Negative, we understand it in the drawing because everything is drawn to make it clear better Right, for example, let's draw this curve. I know what's going on Here is the Audi that we named This is a CF-R. What does this mean? Here's how to draw the curve. We like this example because it is very common. This and that are from There are many common examples. Look at what he said, what he said, Mr. What applies to CF when x is positive? I mean when my ex is who he is This is the part that we draw in. In red this is C Ash said and the second part CS is equivalent to CF in terms of the hierarchy axis. When x is negative, how do you guys follow it? This part, this part, this part of us We look again This is how we return CS to CF. For the ordinate axis when x is negative This part is C What part did we get, should we look at it again? As for me, huh, this is a drawing of a CI Sh Kh, the words are not He said, "This is evidence and the party is fair to us." We will protect your soul and then he will be my children again Considering the axis of arrangements, this is Sh What is this? You see, the words do not apply to him. The part we got is a look at it. axis The order of magnitude is now the same The ninth case, the ninth case, he said, when you are naughty The absolute value of the formula is equal to the value of the formula. Look at it. With me This means that we have given the function its full absolute value. Out and we know that the absolute value in The absolute mathematician is always something positive. Always something positive, its meaning is clear in what it means. This is C Ash located above the axis of the intervals. Listen. How do we learn with examples all this? Dina Al-Mahna, I know it's a curve, this is it The curve is the function. What is the function? Come on, let's read the definition and you'll see what it means. CI will insist on applying to CF when CF Positive, okay, when x, when yx, what does it mean? It means the upper part fits on top of each other. This is it This part is meant above the axis of the intervals. We apply, listen to CS, in comparison to CF. For the axis of the intervals, when the AFX is negative, what is it? I did not understand, sir, what does this lower part mean? The observer in relation to this axis of separations I mean the best of you, this is not a curve The function What is the curve of the function? Look at the one above. The top remains and what was below comes out above What is the Dallah curve? This is the Dallah curve. What's wrong, professor? Did we say something? Excuse me, right? Here you go. He was giving us the phrase "Gendarmerie" This is Khaloui, see the comments of the clever ones. The comment if it gives Ash Lax it would be equal to us We are equal to Sh minus the absolute value of Lax Give us the opposite. Let's see his explanation. Ashks minus absolute value Lafix tell me how to draw the curve of the function Right, you are the smart ones Let's go now to the tenth case. The tenth case, what does the x equal to the y minus? The absolute value of x. Look here, here, the value. The divorced woman alone and they gave us Incomplete examples, learn more Here, for example, is my curve. Look with me. My curve is coming up like this [music] This is how the curve comes I know this is it F first Absolute value, mom, you know I told you not to give X first minus X means and we came here And we write what If we write it like this, it will be mine. If x is minus this is when x is equal to Positive, even if we write it in this form. This is the answer. Minus and this minus becomes me, what does Lax equal to us? If Lux is the X Negative health I started to see myself K Nahi symbol The absolute value once gives me F minus X. And you give me an AF Lax Nahwa X Nahwa This is the absolute value Instead of this, you are graduating Find the absolute value and replace it with dh. You will get dh. See what Sari CS applies to CF when X It is negative, so x is negative. Look at the F. LAX equals ASH LI X, which means when it is X Negative means from us and back to this side applies This is it CS applies to CF counterparts relative to the axis. How do you arrange x when it is positive, professor? It means this part is my children, this part is my opinion [music] This is what we call the overall curve we get. This is SI. Come with me and let's repeat this. Which of us applies to him? Huh? Huh? Why? If x is negative, x is negative, which means we apply it to it. This part is a supervisor who will put it in our minds. This will become mine. It is the function curve. Oh, bravo. Let me give you another one. The comments were giving us a lot of value. Absolute love for absolute value lac x value Absolute outside absolute value inside how much here in this This edition of the book addresses this question. like that Ashks minus AF for absolute value Lax, leave it in the comment, it's easy for those who understand this You will understand others Comfort all For all levels in the Akash project Educational, then we come to my children to an important element The last one is the constitutions of changing the advertiser where We talk about the axis of symmetry and the center of symmetry. The three laws for each one of them behind me Here is their explanation in this second edition, Rani. Here on page 18, my children, I will explain this to you. In detail, this is the slant, but we want you to be patient. With me until the end where we talk about the axis Symmetry and its three laws Center of Symmetry The three laws with practical examples graduated I understand very well. Bring a notebook and pen and let's go. We continue, he said, or a teacher will come to the Omega level Point of this level Omi events X zero Zero health about us regarding the teacher or AG We have one more teacher, let's say Omega EG. New teacher in the level or a point of the level Note with me this point or the x-coordinate In the first teacher or EG coordinates in Teacher or AG is X IK where XAR They are younger than Skeel. Its events are X-Magic and Magisk in the teacher Follow this and see this form so we can understand everything. But we want you to focus with me point by point. I have the teacher or AG and I have The second teacher is Awi Ayumi J and I have The point is here at this level. Follow them. With me, it's good now that I see this difficulty changing Teacher, how do we get to this point? It is coordinates for this teacher. Is it black or is its coordinates black? Excuse me, X, let's make it Minsk X Okay, that's right, but as for this teacher, he's the one The coordinates are X Magisk Wag. Magisk, may God have mercy on you. We will repeat this. The point or coordinates are under this landmark. Black is X-Walk young and its coordinates are in This teacher is red and they are X-Magic Wag Magisk now let's come and see how we can get out Here are the coordinates. Follow me on how to change. Teacher, if you become this, ... What is it worth, you clever ones? It's worth it to us. The value is from us to him, whoever she is, see In the mind, it is X zero, which is from us This is here x zero our morning is x zero Plus from us here we return this distance from Shouf This is equal to this plus this, from us to here, from us to here What are they? What are they? What is X? Magisk huh this is for you x Magisk Come on, let's go What is it equal to? It is equal to us. This is the A, which is A, zero. Plus what is this plus? she What's up, professor? The high school professor is back. I understand. Focus with me on this point. Her X is from here to here, this is the X Musk What is equal to this plus this is equal to us, this is from here She is X Zero, but this distance, these coordinates from Here, this comma, what will it do to us now? You will make us equal to the big one, which is this one This is the equivalent of what we have. This is the equivalent of what we have. Zero plus this value in the new teacher Hey Magisk, my little X equals our X. Zero plus big x and a is equal to aar zero Plus R Big if huh and I change the teacher Audi focus It is not logical if this x equals x zero Which is the big omega plus x comma? And it equals zero, which is ohmic in order Plus a big one you can even save now The axis of symmetry is because this is the whole service for us. We need it in the center and the axis is about us Symmetry of a function DF defined on the domain DF It means that you have knowledge of the CF field and its representation. The statement in the teacher or Egy said to prove that The straight line DT has the equation x equals a Axis of symmetry for CF There are three ways of birth My girls, don't worry too much about this. There are three ways. The first way is to change the teacher. We take advantage of this. The relationship, see with me carefully this stage Stage B: Writing the CF equation in the teacher Omega AG focus on the mind then the gym prove The function f is even in this first stage. We are fully committed to the application. Don't worry. Nothing wrong with it. Now let's move on to the second method. Second for every x of DF Wax Plus A belongs to IF where IF is not minus X We are equal to AF plus X this way Wife, now we go to the third method. For every x of df two a minus x It also belongs to DF where DF is for two minus x equals f lax and this is the law Most used in tests and in Baccalaureate is this the third case if Dry the first way This is the teacher's second method. The third way is this, and this is the most common. Use this. Who is this axis of symmetry? Let's go. Now to the symmetry center and then we turn Examples of people who graduated fully understand and that is what we do. Important note: Intercede for the function because it will be gone later. We need the even function and the odd function The function if x belongs to df and minus X belongs to DF where DF minus X If the function f is even, then the function f is equal to this. Its limit and its curve are even functions. symmetrical with respect to an axis Arrangements, but if X belongs to DF So minus X also belongs to DF and DF minus x equals minus f x van f Individual and curved graph of symmetry with respect to The principle or is it true that we need this now? The symmetry center is the most used and most Half a lot in the exercises that are the most important Knowledge of DF and CF representation in Teacher to prove that the point Omega has The coordinate AB is the center of symmetry of CF there. Three possible ways Mama center of symmetry The first way is to change the teacher who This is how to write the CF equation in the teacher The new one is Omega EGG Proof that The function f is an odd function. The center of symmetry is a function. Evenness of the axis of symmetry, evenness of the center function Symmetry is an odd function. This is the way number one. The way the wife is that X belongs to DF And two a minus x belong to IF where IF is not Plus F La Plus X Plus F La Minus X We are equal to two in this way alone Use in tests and baccalaureate This is the third way X belongs to DF And two a minus x belongs to DF where DF For two, a minus AXS plus FDX We are equal to each other in these two, for example, the laws are yours My sons and daughters, I love you, don't worry, I'm not going We rule this and write this. Your hands have a lot of time. Things are written on the blackboard, you just have to understand them But with practical examples, the information is reinforced. Nice, nice Audi, if now I want my daughters to follow well With practical examples, how do we use these methods? Three, but your love focused if we come application IF function defined on RCF representation Graph in the plane relative to a perpendicular landmark Homogeneous or AG where F Lax is the phrase Its is x squared minus where x is plus Two omega coordinate points one one in The teacher or AG said that the straight line is pointy The equation x equals one axis Symmetry of the CF curve is the word axis of symmetry. Maybe a group, for example, if it was like this, for example, a word Axis means straight. This is the curve. Come It is symmetrical with respect to it, as its equation is X equals us A word about the center of symmetry is a nice center Symmetry is, for example, a point. Our assumption is that this is the Omega point. This will come to you. So sorry center Symmetry here comes the curve opposite to us For example, this is how it comes, and for example, it comes like this, so that Symmetrical with respect to this point, let's see which A point of this and that is symmetrical, this and that are the same We are symmetrical in this regard so that we can learn the idea. I mean, you know what I mean by this now, but be patient You are worried with me, you are worried, the lesson is already Sit down and don't worry, you know that the straight path is straight The equation x equals one is the axis of symmetry. We will start with the first method, changing the teacher. First Audi if If the axis is broken Symmetry for who is not If we can now go to the first method and try We learn three things: Be patient first, then we go We write what he says here is X, hi, hi, X Zero zero cm here give me back one and here one this This is what I recommend. This is good. You can see it in it. I am X in mathematics, what's wrong with you? We say "Effex" when we mean "Good morning" This is how Mia Ray is written, X equals one Plus X Magisk and I have a ra equals one plus a Magisk This is how it is written, may your souls rest in peace And we learn This is this is this is what this is, that means you become Look at it differently, IF LAX, may God have mercy on your parents Follow this, this, this, this means, good morning, Afx We put it here, it becomes equal to x, excuse me, excuse me, one Plus a Majestic health, Afx, where are you? Where are you going? This is x squared Minus two x plus excuse me we write it always Small if he meant small two x plus Two equals one plus R-Magic but Look with me carefully, look at the idea X Minsk Look what Najib and I will do to compensate Here we make up here, come back, Mr. X, small One plus big x equals us One plus one is big as we know that FLAX Hi, this is my daughter. Bring her to me, my servant. Mia and my servants learned this spirit and brought it here Put it here, when you put it, it will be like this for me Lux equals us one plus a Magisk now this We can replace the minus one with one plus one. Plus X Magisk becomes one plus X All of this is like this, your magic is missing, where is there an extra one? X Magisk plus two equals one plus a Magisk So see, you will see the CF equation written In the new teacher health publish this first box Plus the square of the second plus twice the product of this Magisk is missing Two minus two x plus two equals us One plus Akik Magic you woke up see what's going on My children, I don't have to worry about you This goes with this This goes with this and this goes with this And tell me what's up with us, Eric Magisk We equal X Magisk huh and we write equation CF in the new teacher this is a proof If the function is even in the new parameter, it means Her phrase, huh? Where do you mean, Audi, we have completed this? The second stage is to prove that I am Washing This phrase is proof that God exists. Even function but in the new teacher we know If X belongs here, it is defined on R to R. So also minus X belongs to Rani Magisk Belongs to AR so what do you see that Mia is missing? X-Magisk All Square equals X Magisk Square Marriage is what we said about it that it is an F minus X Equal to F Lux with the definition set Symmetrical with respect to zero minus go to that Substitute here with a minus x squared and leave it the same. X square directly click and say from it what is it Dala My new teacher is married to me Oika Ai From him and from him what did I do and from him I did axis symmetry Who is the curve for? We will do it again, sir. If you understand, bravo. First, we must write the expression for the function. IF IN THE NEW TEACHER I went out after we went to prove that she is married Set it as a pair for servants Directly click on the axis of symmetry This way The first way, the second way, here it is, we said the same We will learn everything, God willing. The second method is: For every X belongs from DFNX Plus I have a soul that belongs to me. Two of us here, X equals us, A here, how much? One saw, one saw, for your information, only one saw, it is correct to say X belongs to RX Minsk And x plus one belongs to r, where see Mia, where is Wash for the one missing X? We consider it a soul checkpoint, we consider it, we consider this side We consider this direction equal and we say that it is the center. The axis of symmetry is correct. What does it mean to me? You can replace it with one minus x, one minus x. One minus x becomes one minus x squared minus two times one minus x then plus Two becomes ours We are equal to what is equal to the square of the first plus the square of The second is missing twice product minus two then plus two x then Plus two equals x squared I have this with This goes and I have this, and with this goes, I have this left x squared plus what plus one who is this Oh, you are a lost child X we go calculate DF to 1 plus XF One plus x equals ng. Here we substitute one. Plus X plus X plus X plus X plus x squared minus two times one plus x plus two becomes the square of the first plus The square of the second plus twice the product then minus Two minus two x plus two I have this With this, with this, with this, it will go and become equal One plus x equals what, excuse me, one Plus x squared look at this, look at this If the load is minus x, we get x squared plus And I have a valley plus X Our output is one plus x squared. How does that mean? FYI, it's the same as x squared plus one. What is the reason for one minus X? We went out We went out with the F1 plus X equals us F for one minus X And from it Axis of symmetry for CF. How many seconds does this method take? A thousand thanks to every student who follows Now let's go to the third method. Which is the most used in tests? Bachelors is specialized in bachelors which is The method is the same scenario. This is the method. three Three X's belong to R And two minus two a minus x two a minus x Which is two, here you have two children In one minus X belongs to R professor what I did not understand where this came from. How many people put this here? Put it here and replace it with the right one, so this will become two for me I swear to God, whoever does not follow, I am missing an X. The year terminal ends the expensive and cheap with this Things are right With us it becomes me like this IF for two minus X Equal to one here, it becomes two Minus X, we have to consider it as her share, and this is how How can you come back to me like this? Substitute two here, minus one. x2 minus x where is minus a morning two minus x squared minus two minus x Plus two equals four plus x square minus 4x minus 4 plus 2x plus 4x equals This is x squared I have this with this with this he will give me Minus two x's and I have this and this goes Come back to me, how many two, and you'll be worth FLX to us? Look WD 2x minus x equals Afx we say and from it Dt axis symmetry How much we have learned from the method Don't change The teacher directed the phrase, look with me carefully After we show the even function in the new parameter That's it The second is F La minus X equals F La Plus X is the third most used method. If two a minus x equals us to f lax with Always two minus x belongs to me F wax belongs to my husband, health this now and my Axis of symmetry, be patient with me, let's add a center Symmetry, be patient with me. Leave the comment and these are my girls. He said we will be patient with you, professor Now let's move on to the second application. Who is talking now about the symmetry center? mental health The first way rule is what is change The teacher Right, if we have my Omega, he said, “Af Dala” Numerical knowledge on AR Mada Valley and CF Its inter-representation at the known level is in The level attributed to a homogeneous orthogonal landmark or Egy Omega coordinate point one one in Teacher or EGY where AFX equals us X plus One over x minus one said between the point What is the point Omega center of symmetry for L C? Where is Omega coordinate we said one by one We follow Audi point Point A where here let me phrase the function Excuse me, this is an X minus X. Here are some examples. Just right, let's go first if the way We said one Proof a B An Omi Symmetry Center Right, first we go to see what's here. We said, "Omi, huh?" One, notice that when we say x, we say x equals zero. Plus X + Magisk + Wa = 0 + Magisk Where they focused with me, we said that this and that are X zero zero cm this We write one here and one here One also we said that if lax is a small AFX Always Afx Ray equals us, that means you are smart We can come here and replace it so it can be like this for me x equals 1 plus x big waf Lux equals us one plus a big note Mia We always say again, listen to what you say. Right, I have my Lux, here it is, I will bring it and put it He has this first point. If he returns to this, bring it back. Put it here, which is X over X minus one. The second thing is that this is the X that equals us. One plus a big X, this is what we bring here We will answer here, see how we will get rid of X Small and small, she remains very big for us Big wax becomes ours and becomes ours plus big x On Najib, that one is here One plus big x minus One equals one plus a big R, that's right I have This goes with this I woke up, this turns into here, my morning is one plus X Big on big x minus one equals us It's so big that you see what I'm doing to you We unify the position, it becomes my X Sorry, one plus x Big minus X big over X equals us A Big Magisk, that's right. Look, look, look. Look, look, don't worry, it's gone now How long will he stay here? One, look how I've been here. What happened? My function is in the new teacher Hey, this is what we called FLX, big FL Big Lux, we are equal to one X. Oh, look! This is the same script here. Writing the CF equation in the teacher New proof that the function f is odd in The teacher New We return to the individual function, these are the laws Remember them here Give the adjustment if this is where you become Excuse me Big EFFX equals 1 over big X Now we install it correctly. This is the first one with DF. In this case, you will become my star One on x is the inverse of the function. Knowing about yellow health becomes for me and what X we say X belongs to R A large X-shaped star belongs to the R star group. Where what If we minus a big X, its share must be equal to ours. I need Af Lax in the morning. I will go and bring Awad here. In the minus and here in the minus, give me one in the minus Big x is equal to minus one over xx and We are equal, minus the big F-Lux. Look at the DF. Minus x equals minus f x. That's how we say. And from it, Af Dal How is it? [music] Individual Odd, and since the function H is odd, we have proven it to be odd in The teacher New means in the new teacher it became The function has a curve that is symmetric with respect to We start saying From it what and from it Omega center Symmetry of the CF Al-Fatihah, come back to the idea alone Do it again on your own because her share in the tests is right This is the first way to change the teacher. We actually use it a lot to solve exercises. Now we go to the second method and use it as well. In the case of exercises, the third method is: The most common, but we are required to learn For three because it is programmed on us correctly Two of us said X Belongs to DF and see with me here My coordinates are one by one This means that this represents A and this represents B. In the name of God, the Most High. One and one, right? Good morning, we said X belongs To this F and two a means two minus x belongs to DF is AR except for one professor I did not understand Huh? Except how many times one becomes two minus X Belongs to F Wax Belongs to F Where Derq We are going to calculate this side and install it so that When we calculate two minus x plus f2 Plus X, its share must be equal to two BHA Where are you? How many of you are with me? There is only one left. They hit two in my morning, two in my morning, we calculate this branch We must share where we are, where we are wrong, Ha F LAX plus A plus FL LA plus X Plus or minus X equals us Be reasonable, don't worry about anything, just worry about what's wrong One is our fat one minus X and here one is plus X back yad ha f for one plus X plus If one minus x equals two, right? We need to get this to her and get her back to us. If there is one missing, X plus F for one plus X must be half We are equal to two, two, two, how much is it? One here Don't worry, I'll come to your place soon. One minus X One minus X minus One plus one, make up for it here, one plus x One plus x minus one equals what I didn't understand, sir. One plus X, one plus x1 plus a then one minus x1 Minus X one minus X I have this right This one goes and this one goes with this one. Go and see, I'm back. Let me know what you think now If we multiply here by a minus and here by a minus, always This is a rule: multiply here by a minus sign and here by a minus sign. Make you here minus here plus and here plus is permissible To multiply a fraction by the same number in the numerator and in the The denominator but different from zero is multiplied here by I changed the sign and hit here in minus Professor, why do they have the same position? The idea is that it became their place X is my morning minus one plus one x plus one plus X this with this goes X and X is him Two X's plus X's go with this and equals this I have two and my daughter is always upset. She went out. Two, this is what I said to you And from it Omega Symmetry Center for CF Al-Fatehiyah And understand the method of the wife. Now we go to the method. The third one is the most used one I told you about Exams I love bachelors and I want them to be patient with me They graduated with an understanding of this axis, which is where the point lies. The method is complete, God willing. Three I have X belongs to D A minus two x to f where we said the law He says, "If you look at Mia, if two minus X" Plus where What does a minus x mean? Plus, if Lux, her share must be equal to ours, sir I did not understand F Th A minus X plus F Lax We are equal to one another, this is the light No one should worry about Sama, we must have a destiny, let's calculate The side must have its share as well, so that we can be equal. We couldn't find where we were wrong Here we say are we equal to two? We're back, F2 minus X plus FLAX We are equal to two minus x divided by two Minus x minus one substitute here where minus x minus x plus fx which is x over X minus One of these is worth something to me. I have this and you give me this. How long have you been here? We'll hit the same plan here. In minus and here in minus becomes becomes multiplied here In minus morning here minus plus and here becomes here X minus one, sir They have the same position. This plan must be returned to him. The same position, Basir, the process of reduction becomes The denominator is rax minus 1x and 1x is a X minus how much is missing A went out to the subscriber, good morning A in X minus one on X minus one with The function is known to one, so we can reduce it. here And from it Omi center Symmetry for me Ship I was patient and understood the whole axis. I lost my son because of what I lost something These things are not just patience Don't be patient, you will definitely benefit in this life. We highly recommend this book, the second edition. Honestly, it's great There are more than 1000 Black Ra in it There is no exercise or solution here except for the tests. In it 100 without training exercises and so on 134 training tests without the eighties We tell you the second edition for the first time in Algeria The book that will make a difference in your studies For mathematics in the second year of secondary school A book explained in detail, page by page, in an easy way Free methods on Professor Nour El Din's channel The second edition of the Silver Series book What you need in one book, study with ease Trust it and be among the top achievers in all states. Algeria prepared by Professor Nour El Din In cooperation with Akasha team, order it from the library The Akasha Library near you is more than just a house Published with Akasha books, his joy is complete. Baccalaureate in the end, I will take my daughters Please pray for our health and wellness. May God have mercy on the pure one and grant her peace and blessings We love you and we die for you, my son, my daughter who is complete Video Khalili comment Bash We will add the rest of the topics. Peace be upon all subjects. For all levels in the Akash Educational Project