Inverse Functions

Inverse Functions - Inverse Functions To find the inverse...

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Inverse Functions

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To find the inverse of a function we let the original function f(x)=y and we swap x and y and then rearrange to find y. Remember that this new “y” is really not f(x). This is the same thing as rearranging to find an expression for x and then swapping x and y once we’re done. It isn’t important which way you do it.
e.g. 1 Find the inverse of Solutio n: Rearrange ( to find y again ): Let y = the function , swap x and y So, x x f 3 4 ) ( x y 3 4 y x 3 4 x y 4 3 3 4 x y 3 4 ) ( 1 x x f

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e.g. 2 Find the inverse function of Notice that the domain excludes the value of x that would make infinite. 1 , 1 3 ) ( x x x f ) ( x f
e.g. 2 Find the inverse function of Solutio n: Let y = the function: There are 2 ways to rearrange to find x : Either: 1 , 1 3 ) ( x x x f 1 x 3 y

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Either: e.g. 2 Find the inverse function of There are 2 ways to rearrange to find x : Solutio n: Let y = the function: 1 x 3 y 1 , 1 3 ) ( x x x f 1 x 3 y
e.g. 2

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