Hello assalamualaikum warahmatullahi wabarakatuh Hi everyone, welcome to the good education channel in this video we will discuss the composition of functions before we start the discussion, let's support this channel by clicking subscribe like and comment because subscribing is free, the composition of the function of the word composition is actually familiar to us, usually if for example we open a snack or light meal, usually behind it there is a composition, for example garlic, shallots, tapioca flour, salt and so on, so that means the snack or light meal consists of several ingredients that are combined into one product, namely the snack, we are familiar with the word composition, right? Well, if in the composition of functions in mathematics, the composition of functions is a combination of operations of two types of functions fx and GX so that it produces a new function Well, that means if for example we relate it to the example earlier, FX and GX are materials, then later they will be composed so that later it will produce a new function, for example, here is an arrow diagram of paper production, a factory producing paper, of course there are several stages from raw materials to paper products, right? For example, one production step from basic wood materials to semi-finished materials is processed using sophisticated machines with the function formula f, then from semi-finished materials it is processed again into raw materials So paper uses the G function formula for example, this paper production means going through 2 processes, the name for the two processes consisting of FU qf and the G function is usually called the composition function, the composition function is usually written like this, okay, so that it is better understood mathematically, pay attention to the following explanation, for example, it is known that there are two functions fx with GX. Now if we combine these two functions or we compose them, these two function formulas will produce er, the composition of G is written like this, Eko, the position of GX or G composition f x, the shape of the symbol is like this. This is read as F composition G or F Roundabout g f composition GX means then G composition f x, now a small circle like this is usually called composition or Roundabout F composition GX or F Roundabout GX, this means the book combines the function f to the function G, the function f composition with the function G Ma, the shape is like this, meaning Epul, the position of G, the G function is inside the function f, so it is layered, while G composition f x, namely the music is outside the function, the effect is inside, so it is clear, yes, F composition GX means fgx, so the gx function is inside the function f f which is outside G which is inside While for G composition f x means gfx means the function fx is inside the function G or G is outside FX is inside So the function f composition GX is not the same as the function G composition f x even though the formula ingredients are the same for example if it is known that there is a function fx full agenbola855 compose this if we combine it namely Ed then composed with G then composed again with ha then composed with ix100 this means F is the outermost yes then inside it again adage Then inside it again there is a right then inside it again there is ix6 like this Well it means this is layered well like this well this is the most layer with this function well the chair is inside the function H function H is inside the function G function G is inside the function f well like this so it is layered like this onion layered yes the process is layered yes but if for example Jack composition F composition is composition hx100v G is the outermost yes then inside it again there is f inside it again there is a right x1123 well like this well this is the symbol for the composition of the function Well, the process is called the composition of the function while the function that has been made is called the composition function of the substance so the difference between the composition of the function and the composition function to better understand we discuss 15 examples of composition of the function given the formula of the function formula fx = 2x + 3 gx = X has been reduced by 4 hx = x reduced by 2X = X determine 1F composition of GX 2G composition of the effect 3F composition of G composition hx4 ha composition of G composition F X5 F composition of G composition hx6 F composition of decomposition hx7v composition x8q composition fx9 F composition of G composition of rights composition ex-10 F2 11g negative 3 12 FX1 13f composition of G2 14f composition of decomposition of rights negative 1 15 m composition of G composition of rights x reduced by one answer number one eh composition of GX to work on this question Just understand the meaning of the tail of the composition of GX composition of GX that means at outside GX in Hi like this, the steps to work on it are we work on the inside first on the inside, right, there is GX, right So that means we substitute GX into the formula GX the formula is X squared minus 4.1 list f x squared minus 4 well like this the function will be f x squared min 4 we see the function fx = 2x + 3 if this X becomes x squared min 4 here it becomes x squared min 4 means X on the right side also becomes X squared minus 46 in the function fx and 2x + 3 yes it means here it becomes two excesses become this eqwe this means 2x yes 2x eh then add does not mean here add three if x = 2x + 3 if x squared 4 becomes 2 x squared min 4 + 3 see The form is the same 2x + 3 2 eh plus three then we operate again means fish multiplied yes twice x squared 2 x squared 2 times negative 4 negative 8 then add three then becomes 2x squared negative 8 plus 3 negative 5 becomes the composition function F composition gx is 2 x squared minus 5 well easy Okay next number 2 G composition f x Well we interpret this g composition f x that Dedi outside FX inside how to do it do it or change the inside first bye qg the effect is we see the function formula f the effect is 2x + 3 well bless this effect we change it to 2x + 3 then because this means it becomes G so much we see the function formula gx GX = X squared minus 4be here GX well That means the function formula gx we change the x to 2x + 3 then the formula becomes g 2x + 3 = 2x + 3 squared minus 4 nabatieh if GX = x squared minus 4 if g 2x + 3 becomes 2x + 3 squared minus 4na remember yes this means a + b squared right Well that means we are strong Ranggi so 2x + 3 multiplied by 2 x + 3 minus 4like 2X times 2x 4x squared-2x times 3.6 X3 multiplied by 2 x6x three times 39 then minus 40 Dian becomes 4 x squared plus 12x plus five and 94 is 56 neat function formula G composition of f x is 4 x squared plus 12 x + 5 try to pay attention to the results of the composition function eh composition gx is 2 x squared minus 5 while G composition f x is 4x squared plus 12 x + 5 means here it can be seen that rapping the composition of GX is not = G composition f x Even though the ingredients are the same for eh composition G the ingredients are function f and function bit the ingredients for decomposition FB together with function f and function G But if the composition is different then the results will be different Well so it is clear here it can be seen that the composition of the function is not commutative commutative means exchange yes if multiplication. and before for example two times three is the same as three times two right But if the composition of the function is different eh composition G is not = G composition F yes so the composition of the function is not commutative Hi number no eh composition G composition hx means that we use function f function G function HD3 formula naeb composition decomposition hf this means eh the outermost inside there is function G inside there is function H x layered Well for teacher pay attention to this X is the deepest meaning to the left three to the right three yes means like this yes means the way we change the deepest here first yes Deti mgxa2 Allah x minus two means Now we go to the function layer g f is still outside yes we change y x y Hi X squared minus 4 right seconds because here geeky Wow means X2 squared minus 14 to become X2 squared minus 4 like this Okay we process it first on the inside yes because it is not finished it is still F now we multiply X2 squared yes means X min 2 squared = X min 2 times X2 yes means we multiply the square of X times min 2 min two X min 2 times x min 2 X min 2 times min 2 + 4 then becomes x squared min 2 x minus 2X means 4x plus 4 now It means for X2 squared is x squared minus four x + 4 we write here X squared minus 4x + 4 then minus Fadli Hello Mas like this we still process it to become f x squared minus 4x plus 4 minus 4 means zero Yes, you do n't want to write it, it means it becomes the effect of the square of min 4x here F function Means fx x yes we replace it with x squared min 4x the effect function is 2x + 3 if this action becomes x squared min 4x then X which here also becomes x squared min 4x then the formula becomes two times x squared min 4 x plus 3 yes it becomes two times x squared min 4 x + 3 Well look at fx 2x + 3 if this efs so much becomes two so much plus 3D I Max like this okay okay we still process 2ins multiplied by two times x squared 2 x squared 2 times negative 4x negative 8X then add three yes this is the simplest yes Well like this is the result Okay next number 4 composition rights G composition f x means the outermost right inside there is ge inside there is fx12 three Well we replace the formula of the innermost function there is FX siding outside then gfx0 we replace it with 2x + 3 then we process GX only remains outside yes what we replace is GX Kevia TX GX = X squared minus 48 if dandruff does not become 2x + 3 squared minus 4 like this then we process to find the one inside here yes right but outside 2x + 3 squared we calculate first 2x + 3 squared means 2x + 3 multiplied by 2 x + 3 twice 2x 4x squared-2x multiplied by 36 X3 times2 x6x three times 39 well it will be 4 x squared plus 12 x + 9 yes then 2x + 3 squared becomes 4 x squared + 12 x + 9 then minus 4/5 Let's still process it yeah there is outside then this becomes 4 x squared plus 12x plus five understand this is already simple means this becomes hx yes but the action becomes 4 x squared plus 12 x + 5 means we see the function H the function of H is x minus two Well because this effect becomes 4 x squared plus 12 x + 5 then it becomes 4 x squared plus 12 x + 5 minus Hi mamakah becomes 4 x squared plus 12x plus five minus two is three Well like this well That means the composition right of the FX decomposition is 4 x squared plus 12x plus three Well make sure here the composition function F composition G composition ha the result is 2 x squared minus 8 x plus 3 while the composition right of G composition f x the result is 4 x squared plus 12 x + 3 the ingredients of the formula are the same efs composition decomposition ha the ingredients function f function G chair ha ha composition G composition F is also the same the ingredients are the delete function IG and function f But if the way of composing it is different then the result of the composition function is clearly different yes this is 2 x squared minus 8 x + 3y four this is 4 x squared plus 12 x + 3 different right Well like that yes again yes it means this composition function is not commutative hopefully it can be understood now continue number five number five F composition G then composed with the function H Ma Means there is a composition function F composition G then composed with the function H means we have to First look for the composition tab get yes earlier the tail position of G exitu is F then GX then we change to x-nya x outside Later it seems to be X squared minus 4/5 Hi well then we see the function f 2 x + 3 means it becomes two XE this is x squared minus 4 then add Hi Keh mati we multiply Gan means 2 x squared minus 8 plus three then it becomes 2 x squared minus 5 well this is the GX composition formula well then we compose it with the function of rights means F composition of G is composed with the function H x = f composition of G outside and inside there is the function hx well like this Eh composition of G outside Hi hx in Eko's heart the position of G remains outside hfgm we change the rights is x minus two boxes x minus two well we have the formula f composition of GX yes 2 x squared minus 5 here F composition of GX Min 26 means X which is at the tail of the G position we replace with X minus opened then it becomes two times X2 squared minus 5 we first describe X min 2 squared X2 squared X min 2 times X min 2 X times x squared X times min 2 min two X min 2 times x min 2 X min 2 times min 2 + 4 then becomes X squared minus 4x + 4 well That means X2 squared is hi eh square minus 4x + 4 then minus 5 mata2in es multiplied means two times x squared 2 x squared 2 times negative 4x negative 8 X2 times 48 then minus 5 so it becomes 2 x squared minus 8X 8530 k-pro musru sih for F composition G then composed again with function H is 2 x squared minus 8 x + 3 ah Mecca eps composition decomposition hx is 2 x squared minus 8 x + 3y Hi well like this next Number 6 Number 5 I deliberately did not delete because we want to compare the iPhone position G composed with the h&f function composition decomposition hat how will the results be Well because these ingredients are the same fgh this is also fgh the order also the same as fgh fgh only different in the grouping yes brackets like number 6 tail position G composition right well That means here we do what I miss decomposition Ha means we look for first okay composition hxd2 composition Hai that means G2 rha X inside then we replace the function formula that is in the innermost layer haksan seconds so outside hxh we change it to Oh means the formula becomes gx2 we see the function GX GX x squared min 4 means if the es becomes M2 this also becomes M2 then it becomes X2 squared minus 49 right we Describe this X2 squared X2 squared like that means X min 2 times X min 2 x * x squared X times min 2 min two X min 2 times x-2 x-2 times this 2 + 4 so it becomes X squared minus 4x + 46 then X2 squared this becomes x squared min 4 x + 4 then minus 4x squared minus 4x4.com angin 400 means no need to write the name of the function formula G composition ha is extracurricular more or less i4x Now next we just determine F composition composition of the right position only has been obtained then it becomes eh composition of decomposition hx03f outside decomposition hx inside Well like this yes means we replace the decomposition hx Earlier it was searched yes in the composition of the right is x squared min 4x means here F so much we see the function formula f function formula f 2 x + 3 if acne becomes x squared min 4x then this becomes two times x squared min 4 x + 3 this becomes two times X squared minus 4x plus three yes adjust the form Hi 2x + 3 2 so much plus three then two we multiply twice x squared 2 x squared 2 times negative 4x negative 8X then plus three Well this is the simplest right means this The function formula so the function formula f composition G composition hx is 2 x squared minus 8 x + 3y composition G composition of Right is 2x minus 8X plus three Well pay attention here was the discussion of function number 5 eh composition G then composed with function H the result is 2 x squared minus 8 x + 3 then question number 6 eh composition decomposition hack.exe turns out the result is the same, namely 2 x squared minus 8 x + 3 yes Well this is the same matter fgh this is also fbh the difference Wow which one is done first if this is done first composition panel Dik if this is done first decomposition rights turns out the result is the same Well from here it means that the composition of the function is associative associative is grouping yes So if for example it is grouped the result is the same Well then the composition of the function is associative question number 7 f composition it's Well that means this is the FC function the effect Nia this er then the function this is the identity function sure fish we have discussed nyaut is the identity function well if a function is composed with the identity function here pay attention to what the effect is like F composition GX that means FB outside eek inside then etop outside oil we replace with voer kwik kwik = X means the effect is X6 will become FX FX itself is 2x + 3 well it turns out the effect is when the function f composed with the identity function then the effect function remains more here so the property applies if a function is composed with the identity function Then the result is the initial function er the first function cache like Number 8 for example ih composition FX means outside the effect inside then what remains outside the effect we replace with the function fx 2x + 3 name if for example i2x + Hi because the function is X means the es becomes 2/3 will then 2.3 is 2x + 3 Well try to see the same result Yes function f is composed with the identity function in the form of x = x it is still the function f then function i as the identity function is also composed with the function f still the result function f Well then here the property applies if a function is composed with the identity function Then the result is the function itself also applies the property for the composition of functions with this identity function is commutative yes tail position X = icon position fx on will previously previously in the composition of the function the commutative property does not apply but if this function is multiplied by the identity function then here there is Julian yes this applies the commutative property well like that okay then o9f composition G composition ha composition IX means this we will interpret that this means e most cave in it again adage in it again there is in it again there is IX well like this okay then we do the deepest part of the world I Agya E remains outside gw remains outside hal remains outside ih we replace it with Hai mah pop this then now the deepest is hxh means we replace the right means er remains outside gw then the right we replace the right is x minus two means the right is x minus two Well like this well then now we mean replace gx2 F remains outside namely G2 which is replaced we see the function gx the function gx is X squared minus 4. here the es is X2 means X2 squared minus 400 like this X2 squared minus 49 we describe this means at remains outside we describe X2 squared that x squared min 4 x + 4 then minus 46 will have a strong effect other men 4x4.com 40 yes No no need to write the name will be the effect of the square min 4 expert we see the fx function yes fx = 2x + 3 at me this then becomes two this 2 x squared minus 4 x plus 3 Well that means twice x squared 2 x squared 2 times negative 4x negative 8X then plus 36 means this eh composition G composition ha composition is 2 x squared minus 8 x + 3y Hi Number 10 determine es2na for F2 means the value of the fx function for x = 2 means that means we see the net fx function if F2 means two times two + 3 like that yes more two times two plus three Well two times 24 plus three means the value of f2 is 10 11 Determine G negative 3G negative 3 means the function G where x is negative 3 correct the function gx seconds negative 3 means negative 3 squared minus 14 like this yes then negative 3 squared is 9 minus 4 then Gene occult three the result is 94 which is five then number 12fx plus one well That means this see the fx function the effect is 2x + 3 he said Eh this is explore one so this becomes two times x + 1 + 3 yes two times x + 1 + 3 Play music times means two times ex2f two times 12 + 3G you become 2x plus five well like this then number 13 F composition G two means the composition function for eh composition G where x is worth 2 means we first determine the function formula F composition GX right means F outside DX inside then we will do the inside first That means the effect remains outside the multiplication we replace with the function gx x squared min 4 Well after that means the effects are 2x + 3 x squared min 4 then it becomes two times x squared min 4 plus three then this is multiplied by two times x squared 2 x squared twice negative 4 negative 8 plus 36 will be 2 x squared min 8 plus 3 means this 5 vegetable The function formula for F composition GX if we are asked to determine the f-con position G2 means F composition G where x is two tired we write F composition G 2 = two times two squared yes because the ice will be two yes then minus 5 we will fade first this means two times two squared-4 yes means two times 488 minus 5 means three So the value of F composition G 2 is Hi mah like this next Number 14 f composition G composition of negative one this means the tail position G composition hx5 naex is negative one means we have to first find the composition function formula for F composition G composition hx well composition G composition hx means F outside then inside there is ge inside there is ha then we do the deepest first here means the position is hx means F remains outside then G then hxc we replace it with the function H function only is FB minus two think bag and his side x minus two then means the deepest now gx2 means F remains outside gx2 we see the function gx function gx squared min 4 he said X2 means X2 squared minus 40 you more X2 squared minus 4tak then we break this down first Means at remains outside X2 squared that x squared min 4 x + 4 then minus 4K then we calculate f x squared min 4 X4 minus 4 that 001 is written then the effect of square min 4x means we see the function of the effects of 2x + 3 x it says x squared min 4 means this becomes x squared min 4 yes then f x squared min 4 x is two times x squared min 4 x plus 3 then we multiply this twice x squared 2 x squared 2 times negative 4x negative 8X then add three Well this is the composition function formula F composition G composition hx what is asked is the composition G composition negative one means this means the value of x for this composition function is negative one means we write F composition G composition negative 1 = well That means the formula for the composition function is said to be the value of x negative 1 then we change X which becomes negative one negative 1 then it becomes two times negative 1 squared minus 8 times negative one plus three understand times negative 1 squared means priority negative 1 squared first negative one the code is negative one times negative one negative times negative becomes positive means it becomes two times one yes means two then negative eight times negative one negative times negative is positive second positive 8 then added three means the result is 26 plus 3 more than 13 So the value of F composition G composition right negative 1 is 13 this is the result is Miss Well then for number 15 means number 15 the method is the same yes because the composition function formula will be the same efs composition G composition hf6 decomposition position ha equalize only here the difference is in the x value if 14 the value is negative one if at number 15 XX1 means the way to do it is the same yes means this number 15 this x is said x min 1 how to find the composition function formula F composition G composition is only exactly the same yes means we just determine the effect of composition G composition ha times x-men one means we look at this function F composition G composition right duek webadmin account x + 3 right Well the x is x min 1 then it becomes two times x min 1 squared minus 8 times x min 1 Hi then plus three Well like this then we describe this right X1 squared we describe it as x squared min 2 x + 1 minus eight times x8x negative eight plus three yes then this is two means we multiply to in yes two times x squared 2 x squared 2 times negative 2 x negative 4X 2 times 12 then the negative We also multiply it into negative times 8X negative 8X negative times negative 8 means positive 8 then add 3 Hi Ratih 2 x squared min 4x Min 8X means min12 X2 plus 80 plus three Means 13 So the value of the function f composition G composition hx1 is 2 x squared minus 12x plus 13 so the value is 2 x squared minus 12x plus 13 so like this