Answer
(a) $\frac{1}{4}x+\frac{5}{4}$
(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 $f(x)=4x-5$ is one-to-one. Find the inverse as the following: $y=4x-5\longrightarrow x=\frac{y+5}{4}\longrightarrow f^{-1}(x)=\frac{x+5}{4}=\frac{1}{4}x+\frac{5}{4}$
(b) see graph
(c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.
