Answer
(a) $ f^{-1}(x)=\frac{1}{x}+3$
(b) see graph
(c) $f(x)$ domain $(-\infty,3)U(3,\infty)$ and range $(-\infty,0)U(0,\infty)$, $f^{-1}(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,3)U(3,\infty)$.
Work Step by Step
(a) This function $f(x)=\frac{1}{x-3}, x\ne3$ is one-to-one. Find the inverse as the following: $y=\frac{1}{x-3}\longrightarrow x=\frac{1}{y}+3\longrightarrow f^{-1}(x)=\frac{1}{x}+3$
(b) see graph
(c) $f(x)$ domain $(-\infty,3)U(3,\infty)$ and range $(-\infty,0)U(0,\infty)$, $f^{-1}(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,3)U(3,\infty)$.