Calculus: Early Transcendentals (2nd Edition)

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

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises - Page 10: 42


$g \circ f=x^2-4$, $x \in \mathbb{R}$

Work Step by Step

We evaluate the composite function: $g \circ f=g(f(x))=g(|x|)=|x|^2-4=x^2-4$ Since $|x|^2=x^2$ (the absolute value is redundant because squaring makes the resulting value positive). The domain is the set of all real numbers, since the function is defined for all real number values of $x$.
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