Answer
(a) $f^{-1}(x)=\frac{6x+12}{x+3}, x\ne-3$
(b) see graph
(c) $f(x)$ domain $(-\infty,6)U(6,\infty)$ and range $(-\infty,-3)U(-3,\infty)$, $f^{-1}(x)$ domain $(-\infty,-3)U(-3,\infty)$ and range $(-\infty,6)U(6,\infty)$.
Work Step by Step
(a) This function $f(x)=\frac{-3x+12}{x-6}, x\ne6$ is one-to-one. Find the inverse as the following: $y=\frac{-3x+12}{x-6}\longrightarrow x=\frac{6y+12}{y+3}\longrightarrow f^{-1}(x)=\frac{6x+12}{x+3}, x\ne-3$
(b) see graph
(c) $f(x)$ domain $(-\infty,6)U(6,\infty)$ and range $(-\infty,-3)U(-3,\infty)$, $f^{-1}(x)$ domain $(-\infty,-3)U(-3,\infty)$ and range $(-\infty,6)U(6,\infty)$.
