Answer
$f(g(x))=x$ and $g(f(x))=x,$
Work Step by Step
$f(x)=\sqrt[3] {x-4}$ and $g(x)=x^3+4,$
$f(g(x))=\sqrt[3] {x^3+4-4}=\sqrt[3] {x^3}=x$
and
$g(f(x))=(\sqrt[3] {x-4})^3+4=x-4+4=x.$
Thus, $f(g(x))=g(f(x))=x$.
Therefore, $f(x)$ and $g(x)$ are Inverse of each other.
