Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 125: 48


a. $(f o g)(x) = x^{2}$ b. $(fog)$ is discontinuous at $x = 0$.

Work Step by Step

$(f o g)(x) = f(g(x)) = \frac{1}{g(x)} = \frac{1}{\frac{1}{x^{2}}} = x^{2}$ $f(x)$ and $g(x)$ are discontinuous at $x = 0$ because $f(0)$ and $g(0)$ are undefined. This could be explained by using the 9th theorem given in this section which says: "If $g$ is continuous at $g(a)$ , then the composite function $fog$ given by $(fog)(x) = f(g(x))$ is continuous at $a$.
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