Answer
$f(g(x))=f(\sqrt[3]{ x+8})=(\sqrt[3]{ x+8})^3-8=x+8-8=x$
$g(f(x))=g(x^3-8)=\sqrt[3]{(x^3-8)+8}-3=\sqrt[3]{x^3}=x$
There are no values to be excluded.
Work Step by Step
$f(g(x))=f(\sqrt[3]{ x+8})=(\sqrt[3]{ x+8})^3-8=x+8-8=x$
$g(f(x))=g(x^3-8)=\sqrt[3]{(x^3-8)+8}-3=\sqrt[3]{x^3}=x$
There are no values to be excluded.