Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3 Logarithmic Functions - 6.3 Exercises: 59

Answer

$f^{-1}(x)=e^{\frac{x}{2}}+1$

Work Step by Step

Given: $y=2ln(x-1)$ $ln(x-1)=\frac{y}{2}$ $x-1=e^{\frac{y}{2}}$ $x=e^{\frac{y}{2}}+1$ Now, replace the terms to find out the value of inverse function. $y=e^{\frac{x}{2}}+1$ Hence, $f^{-1}(x)=e^{\frac{x}{2}}+1$
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