Question

express the given function h as a composition of two functions f and g so that $h(x)=(f\circ g)(x)$, where one of the functions is $x^7 - 4$.
$h(x)=\sqrt6{x^7 - 4}$
$f(x)=\square$ (simplify your answer.)
$g(x)=\square$ (simplify your answer.)

Explanation:

Step1: Identify inner function g(x)

We are told one function is $g(x)=x^7 - 4$, so this is the inner function that is substituted into f(x).

Step2: Identify outer function f(x)

The outer function takes the result of g(x) and applies the 6th root, so $f(x)=\sqrt[6]{x}$.

Answer:

$f(x)=\sqrt[6]{x}$
$g(x)=x^7 - 4$