Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 420: 40

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

$f(x)=(x-2)^2, x\geq 2,$ $g(x)=\sqrt x +2$ $f(g(x))=(\sqrt x + 2 -2)^2=(\sqrt x)^2=x,$ Domain of $f\circ g(x)$ is $x\geq2,$ $g(f(x))=\sqrt {(x-2)^2} +2=|x-2|+2=x,$ Domain of $g(f(x))$ is $x\geq2,$