Answer
(a) $ f^{-1}(x) =-\frac{1}{4}x+\frac{3}{4}$
(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 $f(x)=-4x+3$ is one-to-one. Find the inverse as the following: $y=-4x+3\longrightarrow x=-\frac{y-3}{4}\longrightarrow f^{-1}(x)=-\frac{x-3}{4}=-\frac{1}{4}x+\frac{3}{4}$
(b) see graph
(c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.