Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.2 One-to-One Functions; Inverse Functions - 5.2 Assess Your Understanding - Page 266: 40


$f$ and $g$ are inverses of each other. The vaules $x\lt2$ are to be excluded.

Work Step by Step

$f(g(x))=f(\sqrt{ x}+2)=((\sqrt{ x}+2)-2)^2=(\sqrt{ x})^2=x$ $g(f(x))=g((x-2)^2)=\sqrt{(x-2)^2}+2=x-2+2=x$ Since for $f(x)$, $x\geq2$, then $x\lt2$ are values to be excluded.
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