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: 85

Answer

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

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.