Answer
See proof
Work Step by Step
We are given the functions:
$f(x)=x^3$
$g(x)=\sqrt[3]x$
Determine $f\circ g$:
$(f\circ g)(x)=f(g(x))=f\left(\sqrt[3]x\right)=(\sqrt[3]x)^3=x$
Determine $g\circ f$:
$(g\circ f)(x)=g(f(x))=g\left(x^3\right)=\sqrt[3]{x^3}=x$
We got:
$(f\circ g)(x)=(g\circ f)(x)=x$
