Answer
$f \circ g, g \circ f, f \circ f, g \circ g$: for all $D_{f\circ f}=\{x|x \in \mathbb{R} \}$,
Work Step by Step
$f(x)=x^3+2$,
$D_f=\{x|x \in \mathbb{R}\}$
$g(x)=\sqrt[3] x$,
$D_g=\{x|x \in \mathbb{R} \}$,
$f(g(x))=(\sqrt[3] x)^3+2=x+2$
$D_{f\circ g}=\{x|x \in \mathbb{R} \}$
$g(f(x))=\sqrt[3] {x^3+2}$
$D_{g\circ f}=\{x|x \in \mathbb{R} \}$,
$f(f(x))=(x^3+2)^3+2$
$D_{f\circ f}=\{x|x \in \mathbb{R} \}$,
$g(g(x))=\sqrt[3] {\sqrt[3] x}=\sqrt[9] x$
$D_{g\circ g}=\{x|x \in \mathbb{R}\}$
