[Music] he local med so needy discus not a neonatal inverse of one to one function a relation reversing so may work dine at that and an universe for example what is the reverse of positivity negative good but sub-process performed by function f of X is called inverse of function X this means that the domain of the inverse is the rings of the original function so rather than a pen non dominant inverse is the range of the original function as a as the definition said reverse and that the range of the inverse is the domain of the original function so it bees are being class you don't mean in rain-snow original function but that means inverse McGrail inverse lung in Delaware and don't mean original function Ranger sir inverse you arrange an original function domain Chester inverse that and Danielle for example we have the original function y is equal to 2x minus 1 so for example my entire table of values from negative 4 to positive 4 if we substitute negative force to the original function the value of y is negative 9 if we substitute negative 3 to the original function the values negative 7 ok same as negative 2 negative 1 0 1 2 3 4 so this is not the body so why so kappa'd kakuni noting an inverse so I know my IRA so much really versatile not a new y that will be the value of x and you X that will be the value of y so in a pocket apollon saying apology Megara how to reverse the original function okay so let's say this is your domain you know X naught in the original function DT can dominate a negative 4 negative 3 negative 2 negative 1 0 1 2 3 4 when I plug that in fact that things are inverse u negative 4 negative 3 negative 2 negative 1 0 Shannon will rain/snow inverse function so bug pop a little italian prèsto K inverse one-to-one function let F be a one-to-one with domain a and range B then the inverse of F denoted as f place the negative 1 so this is the symbol for inverse know it's a function with domain be in range a so again canina known the interchange lengths are defined by function or the inverse function y is equal to x if and only f of X is equal to Y for any Y NP okay a function has an inverse if and only if it is one-to-one ok my inverse landshark topic 1/2 onion function inverting the x and y values of a function result in a function if and only if the original function is one-to-one so what happened an attend one-to-one and give an equation Kappa add numbering exponent okay so DARPA tenesha eBay know it's kinda in general absolute value Union possible the indicia one-to-one for example find the inverse of the function described by the set of ordered pairs we have 1 negative 3 2 & 1 3 3 4 5 5 7 so again I'm gonna win inheritance which the party needs of each ordered pair the original function is that so a mulligan inverse function at n will be negative 3 1 1 2 3 3 5 4 & 7 5 so again this is an example of one to one function bucket then you move along the rule it values wine a pen okay so how about you take nagging one dito if it's a B and indeed a shot one-to-one so alluring in D shaking inverse inverse of 1 to 1 function capital original function is worth the word okay to find the inverse of a one-to-one function given the equation Maritime Putnam sushant being steps first write the function in the form y is equal to f of X next interchange the X and y variables next and is the last have solved for Y in terms of X for example number 1 find inverse of f of X is equal to 3x plus 1 so that is the original function first we need to change f of X into y so muggin y equals 3x plus 1 so finally turning that into f of x and y so now it interchange the variable so you why Kagami nothing X Y or X Gaga we not in Y so magic in X is equal to 3 y plus 1 X sold for y in terms of X so since gala and not in muscle see why Lee but not in C+ one D talk so mugging X minus 1 equals 3 y again I seen Assad not in detail volume of Y so para Makua not in your body now why we need to divide both sides by 3 so therefore I'm dividing both sides by 3 and so 3 y 2 by 3 I'm not eternal my detour X minus 1 divided over 3 so that is the value of y therefore I use in a 10 so dabit morning why are using ulong so that is now the inverse of 3x plus 1 okay Lyla getting it on a simple data pertaining thereto I inverse so the inverse of X is equal to X minus 1 over 3 that and any learning steps may be nominated another example find the inverse of G of X is equal to X cubed minus 2 again your example a given function X cubed minus 3 is a 1 to 1 so therefore LM not enemy function my inverse store again and gagawin k-pop elite Entertain You G of X naught and my interchange the variables you wipe up a lieutenant X young X Papa returned a Y and then solve for y now so our notion of the steps since why you need a hand up not n LeapPad not in Sibylla see negative 2 it will become X plus 2 is equal to Y cube a maritime cube no Marin tae-young cube Jan so I don't go in by cubing metal toy t-cubed inattentiveness a Kabila so mugging cube root of x plus two is equal to y cube soda money array so now well are you three don't sigh mugging expose exponent okay say you nobody nothing cube boom shaka billah para my wallet on three so therefore why now is a cube root of x plus two penny will enter in parenthesis now we're reading tangling in parenthesis cube root of x plus 2 again but a mossad nut is y so he knew root not in the Hat no both side the cube retire so yeah Moroccan salient 3 so many went along you why do mean cube root of x plus 2 therefore the inverse of X cubed minus 2 is the cube root of x plus 2 okay next find inverse of f of X is equal to 2x plus 1 over 3x minus 4 so rational thought major hababam solution the Gagarina 10 wooden steps change nothing young FX naught and sawai Halawa change the variable see my papa returning x human x naught in d top operator not in my next step solve for y in terms of x okay so cross multiplication 2x times 3y minus 4 it anion is equal to 2y plus 1 of course it is distribute not into XD to sell of x times 3y is 3x y minus x times 4 is 4x is equal to 2y plus 1 since this is odd not in see why a nokia our next steps na gagawin app engine igloo group natin along eagle group not engine eagle group not n you my you may eliminate an eagle group not in Jan of course you my wife Cassie why you've seen us old not in so many times why NASA tree XY tapas Tito me why didn't I see a good group not insulin dalawa so Stu Wiley Padma don't Panama Kazama selling it on 3x why Satan a on 3x y -2 y say negative 4x e para bellum agin 4x plus 1 para Mis old nut is CY illa biscotti c white veto the bite not entombed Ella was a wise on my IRA 3 XY divided by 3x salamati Terra - copy the sign - why / is equal to 2 equals copy 4x plus 1 again since why I am sin assault nothing at make a summary why not in a 3x minus 2 he divided not and both side by 3 X minus 2 so therefore cap again avoid not instance a 3x minus 2 + ma TT rainylin is why it on a man 4x plus 1 divide 3x minus 2 so he turning inverse not n so the inverse of function 2x plus 1 over 3x minus 4 is equal to 2x plus 1 over 3x minus 4 ok so that will be the function again so you in person at the end is 4x plus 1 over 3x minus 2 so Shannon game steps the end ok so meconium inverse next example find the inverse of f of X is equal to x squared plus 4x minus 2 first observe the given function this function is quadratic so Hopak quadratic the graph is parabola pinging you bop opposition's a one-to-one function using the horizontal line test hindi therefore this is a quadratic function with a graph in the shape of parabola that opens upward it is not a one-to-one function as it feels no result alike there so indeed nothing mr. Sabzian persica seen is a one-to-one function okay so Tinga and observed nuan given function Peres in dicta in XS ol next find the inverse of f of X is equal to the absolute value of 3x again absolute valley and kappa Greenup not in your absolute value that is letter V but I'll be honest shape no graph and it fails also in horizontal line test so the graph of f of X is equal to absolute value 3x is shaped like a B whose vertex is located at the origin this function fails the horizontal line test and therefore has no inverse okay nothing in my opinion I'll give you one problem solving okay to convert from degrees Fahrenheit to Kelvin the function is K of T is equal to 5 over 9 times t minus 32 plus 273.15 where T is the temperature in Fahrenheit kelvins the SI unit of the temperature find inverse function converting the temperature in Kelvin to degrees Fahrenheit garnet Z function okay we need to look at the inverse okay right the original function next okay so I know many re after that okay McGee kinky nailiang not in shadow we represent K up tsk no Indian Gilligan me tetanus why not lagging f of X when I pretend I'm not in a white Saudi top palette and anything and K so k minus 200 so it taught the 273.15 D but not in dawn so mugging k minus 273.15 is equal to 5 over 9 times t minus 32 next okay since keno who are not in you inverse okay you know who are nothing in inverse so I know I'm money are in a on we need to divide both side by what we need to divide both side by seeking over why not end right by not 5 over 9 okay divide not in both sides by 5 over 9 CC Tunica 5 over 9 right okay so no money are a after that you our equations but in evite nothing and both side by 5 over 9 that will become what okay this one nah okay so can you know what not in universe vomit ah ha ha OH next since quinoa nothing in tea not only but nothing you - 32 disability that will become 9 over 5 times K minus 273.15 plus 32 and the value of that is 9 of five times K minus 273.15 plus 32 and that is also now the inverse function oh this original function so I thought named in the end no no name Indian sauna how to process this problem Panama not in Malayalam on okay like this example determine whether the function below are inverses of each other or not for example my given time function f of X is equal to negative 1/2 X and G of X is equal to negative 2x pinocchio not in my element I turned 11 function at oh I inverse a sad-sack we are going to use composition panel on so you ex not in detour Papa returned not innovation and G of X okay oh let say f of X I'm public user axiom valanor G of X so the main value no G of X negative 2 X so therefore young X new detour Papa returned up in a negative 2x so my concern not a new negative to negative 1 times negative X is positive x so habil annamund u X nah man none gee Papa little nothing of value dang f of X which is negative 1/2 X so therefore u X naught and Papa returned nothing of value now f of X now negative 1 of X so Omar consoles in egged C positive 2 so negative times negative that is positive x kappa equal answer good now using the composition ibiza BN by daddy finish on the two functions are inverses of each other dot and I know Gaga meeting in a composition Parimal a man and a long functional inversely lasat Issa and then kept an equal eundel ah one function a on Ibiza bein in verse Allah says erisa so salomina to tune and KO about inverse of one-to-one function thank you so much and don't forget to Like subscribe and hit the bell boat on to our Walmart channel