Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises: 18

Answer

The solutions are $f^{-1}(3)=1.$ $f(f^{-1}(2))=2.$

Work Step by Step

By noticing that $f(1)=1^5+1^3+1=3$ we get by the definition of the inverse function that $f^{-1}(3)=1.$ For the second part we will use the following property: If $f(x)=y$ then $f^{-1}(y)=x$ so $f(f^{-1}(y))=f(x)=y$. Applying this to our problem: $$f(f^{-1}(2))=2.$$
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