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 - Concept and Vocabulary Check - Page 1160: 2


The statement β€œFor the function $ f\left( x \right)=\frac{1}{x-3},f $ is not defined at $3$, so f is discontinuous at $3$” is true.

Work Step by Step

Consider the function $ f\left( x \right)=\frac{1}{x-3}$, For a function to be continuous at a point a, the function must satisfy the following three conditions: (a) f is defined at a. (b) $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)$ exists. (c) $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=f\left( a \right)$ Since the function is not defined at $3$, so the function does not satisfy the first condition of being continuous. Therefore, the function f is discontinuous at $3$. Hence, the statement is true.
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