Answer
$f^{-1}(x)=\frac{5}{x}-2$
$f(x)$, domain $\{x|x\ne-2\}$, range $\{y|y\ne0\}$,
$f^{-1}(x)$, domain $\{x|x\ne0\}$, range $\{y|y\ne-2\}$.
Work Step by Step
1. $f(x)=\frac{5}{x+2}\Longrightarrow y=\frac{5}{x+2}\Longrightarrow x=\frac{5}{y+2}\Longrightarrow y=\frac{5}{x}-2\Longrightarrow f^{-1}(x)=\frac{5}{x}-2$
2. We can find: for $f(x)$, domain $\{x|x\ne-2\}$, range $\{y|y\ne0\}$,
3. We can find: for $f^{-1}(x)$, domain $\{x|x\ne0\}$, range $\{y|y\ne-2\}$.
