Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 45: 65



Work Step by Step

To see whether $h=f \circ g$ is even or not, let us find $h(-x)$:$$h(-x)=(f \circ g)(-x)=f(g(-x)).$$Since by the assumption $g$ is even, we have$$g(-x)=g(x).$$Thus, we obtain $$h(-x)=f(g(x))=(f \circ g)(x)=h(x),$$so $h$ is even.
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