Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.4 Exercises: 69

Answer

$f(g(x))$ is continuous for all values of $x$ such that $x\ne1$ and $x\ne-1.$

Work Step by Step

Using Theorem $1.12:$ $g(x)$ is continuous for any value of $x$ but $f(x)$ has restrictions: For $f(x)\to x\ne6.\to g(x)\ne6\to$ $ x^2+5\ne6\to x\ne1$ and $x\ne-1.$ $f(g(x))$ is continuous for all values of $x$ such that $x\ne1$ and $x\ne-1.$
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