Answer
$$ f^{-1}(x)=\sqrt{x-1}$$
Work Step by Step
Given:
$ y=x^{2}+1$
We solve for $x$:
$\Rightarrow x^{2}=y-1$
$\Rightarrow x=\sqrt{y-1}$
Interchanging $ x $ and $ y $, we get:
$y=\sqrt{x-1}=f^{-1}(x)$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 372: 19
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