Answer
$f(x)=x^3$ and $g(x)=1+x^2$
Work Step by Step
We wish to find two functions $f$ and $g$ such that:
$H(x)=(f \circ g)(x) =(1+x^2)^3 $
Let us consider
$f(x)=x^3$ and $g(x)=1+x^2$
Then we have the composite function:
$H(x)=(f \circ g)(x) =f[g(x)]=f(1+x^2)=(1+x^2)^3 $
