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