Answer
$f(x)=x^4$ and $g(x)=3x-1$
Work Step by Step
While it is possible that there are multiple ways of expressing $h$ as composites of $f$ and $g$, we can find one solution as $f(x)=x^4$ and $g(x)=3x-1$, such that $h(x)=(f\circ g)(x)$
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