Lesson Finding inverse functions

Finding inverse functions

Problem 1

The given function is 

    f(x) = .


In wording form, it  " adds 2 to x;  then takes square root;  then adds 2, again ".


The inverse function  f^-1(x)  makes the opposite operations in reverse order. 


In other words,  f^-1(x)  makes the following:


    it subract 2 from the argument; then raise to degree 2; then subtract 2:

        f^-1(x) = .    ANSWER

Problem 2

First, the composition  (fog)(x)  is  

    (fog)(x) =  - 3.


In wording form, it is  "take x^3;  divide by 8;  then subtract 3".


The inverse function to  (fog)(x)  makes the opposite operations in reverse order. 


In other words,  (fog)^(-1)(x)  makes the following:


    it adds 3 to the argument; then multiply by 8; then takes the cube root:

        (fog)^(-1)(x) = .    ANSWER