Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Review - Exercises - Page 234: 86

Answer

Given $f(x) = \sqrt x$ and $g(x)= \frac {2} {x-4}$, we need to find the following and their respective domains: a. $\sqrt {\frac{2}{x-4}}$ Domain: (4, ∞) b.$\frac { 2}{\sqrt x - 4}$ Domain: [0, 16) U (16, ∞) c. $\sqrt {\sqrt x}$ Domain: [0, ∞) d. $\frac{x-4}{9-2x}$ Domain: (-∞, 4) U (4, 9/2) U (9/2, ∞)

Work Step by Step

Given $f(x) = \sqrt x$ and $g(x)= \frac {2} {x-4}$, we need to find the following and their respective domains: a. f o g $f(\frac{2}{x-4}) = \sqrt {\frac{2}{x-4}}$ Domain: (4, ∞) b. g o f $g(\sqrt x) = \frac { 2}{\sqrt x - 4}$ Domain: [0, 16) U (16, ∞) (since the denominator can not equal zero, so 16 is excluded) c. f o f $f ( \sqrt x) = \sqrt {\sqrt x}$ Domain: [0, ∞) d. g o g $g (\frac {2}{x-4}) = \frac{2}{\frac {2}{x-4} - 4} = \frac { 2(x-4)}{2 - 4(x-4)} = \frac{2x-8}{18-4x} $ $ = \frac{x-4}{9-2x}$ Domain: (-∞, 4) U (4, 9/2) U (9/2, ∞)
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