Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Inverse, Exponential, and Logarithmic Functions - Exercises - Page 448: 13

Answer

$y=log_3(x+2)$ (exercise 9) and $y=3^x-2$ (exercise 12); $y=log_2(5-x)$ (exercise 11) and $y=5-2^x$ (exercise 10)

Work Step by Step

Inverse functions are symmetric with respect to $y=x$ and satisfy $f(g(x))=g(f(x))=x$. We can determine from the graphs that $y=log_3(x+2)$ (exercise 9) and $y=3^x-2$ (exercise 12) are inverses to each other. Similarly, we can find that $y=log_2(5-x)$ (exercise 11) and $y=5-2^x$ (exercise 10) are inverses to each other.
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