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: 68

Answer

(a) $ f^{-1}(x)=\frac{4}{x}$ (b) see graph (c) $f(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,0)U(0,\infty)$, $f^{-1}(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,0)U(0,\infty)$.

Work Step by Step

(a) This function $f(x)=\frac{4}{x}, x\ne0$ is one-to-one. Find the inverse as the following: $y=\frac{4}{x}\longrightarrow x=\frac{4}{y}\longrightarrow f^{-1}(x)=\frac{4}{x}$ (b) see graph (c) $f(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,0)U(0,\infty)$, $f^{-1}(x)$ domain $(-\infty,0)U(0,\infty)$ and range $(-\infty,0)U(0,\infty)$.
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