Question

watch the video and then solve the problem given below.
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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)=sqrt7{x} ) (simplify your answer.)
( g(x)=square ) (simplify your answer.)

Explanation:

Step1: Define outer function f

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

Step2: Define inner function g

$g(x) = x^4 - 8$

Step3: Verify composition

$(f \circ g)(x) = f(g(x)) = \sqrt[7]{g(x)} = \sqrt[7]{x^4 - 8} = h(x)$

Answer:

$f(x) = \sqrt[7]{x}$
$g(x) = x^4 - 8$