Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.7 The Chain Rule - 3.7 Exercises - Page 191: 6

Answer

$f(x)=x^4, g(x)=\cos x, h(x)=x^2+1$ $f(x)=\cos^4 x, g(x)=x^2, h(x)=\sqrt{x^2+1}$

Work Step by Step

We are given the function: $Q(x)=\cos^4 (x^2+1)$ The choice of the three functions $f,g,h$ so that $Q(x)=f(g(h(x)))$ is not unique. Example 1: $f(x)=x^4$ $g(x)=\cos x$ $h(x)=x^2+1$ $f(g(h(x)))=f(g(x^2+1))=f(\cos(x^2+1))=\cos^4 (x^2+1)$ Example 2: $f(x)=\cos^4 x$ $g(x)=x^2$ $h(x)=\sqrt{x^2+1}$ $f(g(h(x)))=f(g(\sqrt{x^2+1}))=f(x^2+1)=\cos^4 (x^2+1)$
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