Question

express the given function h as a composition of two functions f and g so that h(x)=(f∘g)(x), where one of the functions is $x^3 - 9$.
$h(x)=\sqrt6{x^3 - 9}$
$f(x)=\square$ (simplify your answer.)
$g(x)=\square$ (simplify your answer.)

Explanation:

Step1: Identify inner function g(x)

We are told one function is $x^3 - 9$, so this will be the inner function $g(x)$.
$g(x) = x^3 - 9$

Step2: Identify outer function f(x)

The outer function takes the 6th root of the result of $g(x)$, so we replace $x^3 - 9$ with $x$ to get $f(x)$.
$f(x) = \sqrt[6]{x}$

Answer:

$f(x) = \sqrt[6]{x}$
$g(x) = x^3 - 9$