Answer
(a) $f^{-1}(x)=-\sqrt[3] {x+2}$
(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 $f(x)=-x^3-2$ is one-to-one. Find the inverse as the following: $y=-x^3-2\longrightarrow x=-\sqrt[3] {y+2}\longrightarrow f^{-1}(x)=-\sqrt[3] {x+2}$
(b) see graph
(c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.
