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