Calculus: Early Transcendentals 8th Edition

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

Chapter 1 - Review - Concept Check: 10

Answer

The composite function $f\circ g$ is defined such that $$f\circ g(x)=f(g(x))$$ and its domain is $$\mathcal{D}=\{x\in B|g(x)\in A\},$$ where $A$ is the domain of $f$ and $B$ is the domain of $g$.

Work Step by Step

The composite function $f\circ g$ is defined such that $$f\circ g(x)=f(g(x))$$ i.e. we first evaluate $g$ at $x$ and then we evaluate $f$ at $g(x)$. This means that $x$ has to be in the domain of $g$ and that $g(x)$ has to be in the domain of $f$. We can denote this set as $$\mathcal{D}=\{x\in B|g(x)\in A\}$$ Where $A$ is the domain of $f$ and $B$ is the domain of $g$.
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