Question

watch the video and then solve the problem given below. click here to watch the video. 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^4 - 8 ). ( h(x) = sqrt7{x^4 - 8} ) ( f(x) = square ) (simplify your answer.)

Explanation:

Step1: Identify inner function $g(x)$

We are told one function is $g(x)=x^4-8$.

Step2: Define outer function $f(x)$

Since $h(x)=(f\circ g)(x)=\sqrt[7]{g(x)}$, set $f(x)$ to the 7th root of input.
<Expression>
$f(x)=\sqrt[7]{x}$
</Expression>

Answer:

$f(x)=\sqrt[7]{x}$