Example 12. Find the inverse function of $y=\sqrt{x+5}(x \geqslant-5)$.


Since $y=\sqrt{x+5}$ is a one-to-one correspondence from the domain $\{x \mid x \geqslant-5\}$ to the range $\{y \mid y \geqslant 0\}$, and from $y=\sqrt{x+5}$ we get $x=y^{2}-5$,
$\therefore$ the inverse function of $y=\sqrt{x+5}(x \geqslant-5)$ is $y=x^{2}-5 .(x \geqslant 0)$