Question 1199844
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Suppose f(x) = x/8 -3 and g(x) = x^3
Find (f∘g)^-1 (x)
((f∘g) inverse) (x)
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<pre>
First, the composition  (fog)(x)  is  

    (fog)(x) = {{{x^3/8}}} - 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) = {{{root(3, 8*(x+3))}}}.    <U>ANSWER</U>
</pre>

Solved.