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: 45

Answer

$G ∘ g ∘ f =\frac{1}{x^2-6}$ Therefore the domain is $x\ne+\sqrt 6, -\sqrt 6$

Work Step by Step

$f(x) = |x|$ $G(x) = \frac{1}{(x-2)}$ $g(x) = x^2-4$ $G ∘ g ∘ f = G(g(f(x))) = G(g(|x|)) = G((|x|)^2-4))=G(x^2-4)=\frac{1}{x^2-4-2}=\frac{1}{x^2-6}$ Therefore the domain is $x^2-6\ne0$ $x^2\ne6$ $x\ne+\sqrt 6, -\sqrt 6$
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