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^2 - 5 ). ( h(x)=\frac{9}{sqrt{x^2 - 5}} ) ( f(x)=\frac{9}{sqrt{x}} ) (simplify your answer.) ( g(x)=square ) (simplify your answer.)

Explanation:

Step1: Identify inner function g(x)

We know one function is $x^2 - 5$, so this is the inner function $g(x)$.
$g(x) = x^2 - 5$

Step2: Match outer function f(x)

The composite function $h(x) = f(g(x)) = \sqrt[9]{g(x)}$, so $f(x)$ is the 9th root function.
$f(x) = \sqrt[9]{x} = x^{\frac{1}{9}}$

Answer:

$f(x) = \sqrt[9]{x}$
$g(x) = x^2 - 5$