Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises - Page 44: 51


$h(t)=\cos t$ $g(t)=\sin t$ $f(t)=t^{2}$

Work Step by Step

Separating the function into three processes: $1. h(t)=\cos t$ $2. g(h(t))=g(\cos t)=\sin(\cos t)=\sin (h(t))$ $g(t)=\sin t$ $3. f(g(h(t)))=f(\sin(\cos t))=\sin^2(\cos t)={g(h(t))}^2$ $f(t)=t^{2}$
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