Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.3 The Basic Classes of Functions - Preliminary Questions - Page 22: 3


The range of $ g $ is not in the domain of $ f $.

Work Step by Step

Note that $g=-1-|x|$ must always be negative. Since there are no real roots for negative numbers, the range of $ g $ is not in the domain of $ f $. In other words $f\circ g$ is the empty set (has no values or solutions for any $x$).
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