Answer
(a) $ f^{-1}(x) =-\frac{1}{6}x-\frac{4}{3}$
(b) see graph
(c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.
Work Step by Step
(a) This function $f(x)=-6x-8$ is one-to-one. Find the inverse as the following: $y=-6x-8\longrightarrow x=-\frac{y+8}{6}\longrightarrow f^{-1}(x)=-\frac{x+8}{6}=-\frac{1}{6}x-\frac{4}{3}$
(b) see graph
(c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.