Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.3 The Chain Rule - 4.3 Exercises - Page 225: 13


$f[g(x)]=\sqrt{\dfrac{x-1}{x}}$ $g[f(x)]=\displaystyle \frac{-1}{\sqrt{x+1}}$

Work Step by Step

In the expression for f(x), replace x with g(x) $f[g(x)]=\sqrt{g(x)+1}$ $=\sqrt{\dfrac{-1}{x}+1}$ $=\sqrt{\dfrac{x-1}{x}}$ In the expression for g(x), replace x with f(x) $g[f(x)]=\displaystyle \frac{-1}{f(x)}$ $=\displaystyle \frac{-1}{\sqrt{x+1}}$
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