Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 295: 84

Answer

(a) $(-1,\infty)$. (b) See graph (c) $(-\infty,\infty)$, $x=-1$. (d) $f^{-1}(x)=3^{2-x}-1$. (e) $(-\infty,\infty)$, $(-1,\infty)$. (f) See graph.

Work Step by Step

(a) Use the domain requirement(s) for the function $x+1\gt0$, we have $x\gt-1$ or $(-1,\infty)$. (b) See graph for $f(x)=2-log_3(x+1)$ (c) We can determine the range as $(-\infty,\infty)$ and asymptote(s) as $x=-1$. (d) We can find $f^{-1}(x)=3^{2-x}-1$. In short $x=2-log_3(y+1)\longrightarrow y=3^{2-x}-1$ (e) We can find the domain of $f^{-1}(x)$ as $(-\infty,\infty)$ and range as $(-1,\infty)$. (f) See graph.
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