Answer
(a) $ f^{-1}(x)=\frac{1}{4}(x-2)$.
(b) $f$: $(-\infty,\infty)$ and $(-\infty,\infty)$. $f^{-1}$: $(-\infty,\infty)$ and $(-\infty,\infty)$.
(c) See graph.
Work Step by Step
(a) $f(x)=4x+2\longrightarrow y=4x+2\longrightarrow x=4y+2\longrightarrow y=\frac{1}{4}(x-2)\longrightarrow f^{-1}(x)=\frac{1}{4}(x-2)$. 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.
