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: 12

Answer

(a) $(-\infty,\infty)$. (b) see graph. (c) $(-2,\infty)$, H.A. $y=-2$. (d) $f^{-1}(x)=log_4(x+2)-1$. (e) $(-2,\infty)$, $(-\infty,\infty)$. (f) see graph.

Work Step by Step

Given $f(x)=4^{x+1}-2$, we have: (a) the domain of $f(x)$: $(-\infty,\infty)$. (b) see graph. (c) From the graph, we can determine the range $(-2,\infty)$, asymptote(s) H.A. $y=-2$. (d) $f(x)=4^{x+1}-2 \Longrightarrow y=4^{x+1}-2 \Longrightarrow x=4^{y+1}-2 \Longrightarrow y=log_4(x+2)-1 \Longrightarrow f^{-1}(x)=log_4(x+2)-1$. (e) we can find the domain and the range of $f^{-1}(x)$: $(-2,\infty)$, $(-\infty,\infty)$. (f) see graph.
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