Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises - Page 67: 28

Answer

The inverse function is $~~f^{-1}(x) = -ln(x-1)$ We can see that the graphs are reflections about the line $y=x$
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Work Step by Step

We can solve $f$ for $x$: $y = 1+e^{-x}$ $y-1 = e^{-x}$ $ln(y-1) = -x$ $x = -ln(y-1)$ We reverse the places of $x$ and $y$: $y = -ln(x-1)$ The inverse function is $~~f^{-1}(x) = -ln(x-1)$ When we graph the two functions $f(x)$ and $f^{-1}(x)$ along with the line $y=x$, we can see that the graphs are reflections about the line $y=x$
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