SOLUTION: Suppose f(x) = x/8 -3 and g(x) = x^3 Find (f∘g)^-1 (x) ((f∘g) inverse) (x)

Question 1199844: Suppose f(x) = x/8 -3 and g(x) = x^3
Find (f∘g)^-1 (x)
((f∘g) inverse) (x)
Answer by ikleyn(52876) (Show Source): You can put this solution on YOUR website!
.
Suppose f(x) = x/8 -3 and g(x) = x^3
Find (f∘g)^-1 (x)
((f∘g) inverse) (x)
~~~~~~~~~~~~~~~~~~~~~~~~~

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

Solved.

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