Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Review - Concept Check: 9

Answer

(a) The domain is $A\cap B$. (b) The domain is $A\cap B$. (c) The domain is $A\cap B\setminus\{x_0|g(x_0)=0\}$.

Work Step by Step

(a) We can sum only where both $f$ and $g$ are defined so the domain of $f+g$ is $A\cap B$. (b) We can multiply only where both $f$ and $g$ exist so the domain of $fg$ is $A\cap B$. (c) We can divide only where both $f$ and $g$ are defined BUT since we cannot divide by zero we have to exclude all points $x_0$ such that $g(x_0)=0$ which can be written as $A\cap B\setminus\{x_0|g(x_0)=0\}$.
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