Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 418: 62

Answer

(a) $ f^{-1}(x) =-\frac{1}{6}x-\frac{4}{3}$ (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 $f(x)=-6x-8$ is one-to-one. Find the inverse as the following: $y=-6x-8\longrightarrow x=-\frac{y+8}{6}\longrightarrow f^{-1}(x)=-\frac{x+8}{6}=-\frac{1}{6}x-\frac{4}{3}$ (b) see graph (c) $f(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$, $f^{-1}(x)$ domain $(-\infty,\infty)$ and range $(-\infty,\infty)$.
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