Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 41

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

$f(x)=\frac{1}{x},$ and $g(x)=\frac{1}{x}$ $f(g(x))=\frac{1}{\frac{1}{x}}=x,$ Domain of $f(g(x))$ is $x\in \mathbb{R} \ne 0$ $g(f(x))=\frac{1}{\frac{1}{x}}=x$ Domain of $g(f(x))$ is $x\in \mathbb{R} \ne 0,$