Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 420: 39

$f(g(x))=x$ $g(f(x))=x$

$f(x)=x^3-8,$ $g(x)=\sqrt[3] {x+8},$ $f(g(x))=(\sqrt[3] {x+8})^3-8=|x+8|-8=x$ Domain of $f\circ g(x)$ is $x\in \mathbb{R}$ $g(f(x))=\sqrt[3] {x^3-8+8}=\sqrt[3] {x^3}=|x|=x$ Domain of $g\circ f(x)$ is $x\in \mathbb{R}$