Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 24

Answer

$f^{-1}(x)=e^{x^{1/2}}$

Work Step by Step

Given: $y=(lnx)^{2}$ , $x\geq1$ $\sqrt y=lnx$ $x=e^\sqrt {y}$ or $x=e^{y^{1/2}}$ Now, replace the terms to find out the value of inverse function. $y=e^{x^{1/2}}$ Hence, $f^{-1}(x)=e^{x^{1/2}}$
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