Answer
(a) $ f^{-1}(x)=-\frac{3}{x}$.
(b) $f$: $(-\infty,0)U(0,\infty)$ and $(-\infty,0)U(0,\infty)$. $f^{-1}$: $(-\infty,0)U(0,\infty)$ and $(-\infty,0)U(0,\infty)$.
(c) See graph.
Work Step by Step
(a) $f(x)=-\frac{3}{x} \longrightarrow y=-\frac{3}{x}\longrightarrow x=-\frac{3}{y}\longrightarrow y=-\frac{3}{x}\longrightarrow f^{-1}(x)=-\frac{3}{x}$. Check $f(f^{-1})=x$ and $f^{-1}(f)=x$
(b) Domain and range of $f$: $(-\infty,0)U(0,\infty)$ and $(-\infty,0)U(0,\infty)$. Domain and range of $f^{-1}$: $(-\infty,0)U(0,\infty)$ and $(-\infty,0)U(0,\infty)$.
(c) See graph.
