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: 48

Answer

$(G ∘ G)(x) =\frac{x-2}{-2x+5}$ the domain is $x \ne 2.5$

Work Step by Step

$G(x) = \frac{1}{(x-2)}$ $(G ∘ G)(x) = G(G(x)) = G(\frac{1}{(x-2)}) =\frac{1}{(\frac{1}{(x-2)}-2)}=\frac{1}{\frac{1-2x+4}{x-2}}=\frac{1}{\frac{-2x+5}{x-2}}=\frac{x-2}{-2x+5}$ Therefore the domain is $-2x + 5 \ne 0 $ $-2x \ne -5 $ $x \ne 2.5$
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