Given the following function, $h ( x )$, find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$.
$h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$
A) $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$
B) $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$
C) $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$
D) $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$
E) $f ( x ) = \sqrt [ 3 ] { x - 11 } , \quad g ( x ) = x + 11$

Question

Quizplus · Accepted Answer

Function $f(x) = \sqrt[3]{x - 11}$ and $g(x) = x^2$ work together because when $g(x) = x^2$ is substituted into $f(x)$, it results in $f(g(x)) = \sqrt[3]{x^2 - 11}$, which matches $h(x)$.

Given the Following Function h(x)h ( x )h(x) , Find Two Functions

Given the Following Function $h ( x )$ , Find Two Functions