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 - Chapter Test - Page 372: 13


(a) $(2,\infty)$. (b) see graph. (c) $(-\infty,\infty)$, V.A. $x=2$. (d) $ f^{-1}(x)=5^{1-x}+2 $. (e) $(-\infty,\infty)$, $(2,\infty)$. (f) see graph.

Work Step by Step

Given $f(x)=1-log_5(x-2)$, we have: (a) the domain of $f(x)$: $(2,\infty)$. (b) see graph. (c) From the graph, we can determine the range $(-\infty,\infty)$, asymptote(s) V.A. $x=2$. (d) $f(x)=1-log_5(x-2) \Longrightarrow y=1-log_5(x-2) \Longrightarrow x=1-log_5(y-2) \Longrightarrow y=5^{1-x}+2 \Longrightarrow f^{-1}(x)=5^{1-x}+2 $. (e) we can find the domain and the range of $f^{-1}(x)$: $(-\infty,\infty)$, $(2,\infty)$. (f) see graph.
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