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: 41

Answer

To form f[g(x)], in the expression defining f(x), $\bf{ \text{ replace } x \text{ with }g(x).}$ (sample answer)

Work Step by Step

To form f[g(x)], in the expression defining f(x), $\bf{ \text{ replace } x \text{ with }g(x).}$ For example, if $f(x)=x+1, \quad g(x)=\sqrt{x},$ then $f[g(x)]\quad =g(x)+1\quad =\sqrt{x}+1$ $g[f(x)]\quad =\sqrt{f(x)}\quad =\sqrt{x+1}$
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