Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.3 - Limits and Continuity - Exercise Set - Page 1160: 8


No, the function $ f\left( x \right)=\frac{x+7}{x-7}$ is not continuous at $7$.

Work Step by Step

Consider the function $ f\left( x \right)=\frac{x+7}{x-7}$, First check whether the function is defined at the point $ a $ or not. Find the value of $ f\left( x \right)$ at $ a=7$, $ f\left( 7 \right)=\frac{7+7}{7-7}$ The function is not defined at the point $7$. Thus, the function do not satisfy the first property of being continuous. Hence, the function $ f\left( x \right)=\frac{x+7}{x-7}$ is not continuous at $7$.
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