Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 86

Answer

(a) $(-\infty,\infty)$. (b) See graph. (c) range $(-\infty,0)$, H.A. $y=0$. (d) $ f^{-1}(x)=log_3(-x)-1$ (e) domain $(-\infty,0)$, range $(-\infty,\infty)$. (f) See graph.

Work Step by Step

(a) Given $f(x)=-3^{x+1}$, we can find the domain $(-\infty,\infty)$. (b) See graph. (c) From the graph, we can determine the range $(-\infty,0)$, asymptote(s) H.A. $y=0$. (d) $f(x)=-3^{x+1}\Longrightarrow y=-3^{x+1}\Longrightarrow x=-3^{y+1} \Longrightarrow y=log_3(-x)-1 \Longrightarrow f^{-1}(x)=log_3(-x)-1$ (e) For $ f^{-1}(x)$, we can find the domain $(-\infty,0)$, range $(-\infty,\infty)$. (f) See graph.
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