Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Problem Statement:**
Use **interval notation** to indicate where \( f \) is continuous.
**Function Definition:**
\[ f(x) = \sqrt{x - 3} \]
**Task:**
Determine the domain of continuity for the function \( f(x) \). Enter your answer in the space provided.
**Explanation of the Mathematical Concept:**
The function \( f(x) = \sqrt{x - 3} \) involves a square root, which is only defined for non-negative numbers. This means that the expression inside the square root, \( x - 3 \), must be greater than or equal to zero for the function to be continuous.
Solve the inequality:
\[ x - 3 \geq 0 \]
\[ x \geq 3 \]
Thus, the function \( f \) is continuous for all \( x \) in the interval \([3, \infty)\).
**Domain of Continuity:**
Enter the domain of continuity below:
\[ \text{Domain of continuity: } [3, \infty) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f1c68a1-c113-41cc-b0cf-42f2666e5687%2Fc70176ca-7329-4c7a-ad1d-3a94846e0987%2F12515nh_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Use **interval notation** to indicate where \( f \) is continuous.
**Function Definition:**
\[ f(x) = \sqrt{x - 3} \]
**Task:**
Determine the domain of continuity for the function \( f(x) \). Enter your answer in the space provided.
**Explanation of the Mathematical Concept:**
The function \( f(x) = \sqrt{x - 3} \) involves a square root, which is only defined for non-negative numbers. This means that the expression inside the square root, \( x - 3 \), must be greater than or equal to zero for the function to be continuous.
Solve the inequality:
\[ x - 3 \geq 0 \]
\[ x \geq 3 \]
Thus, the function \( f \) is continuous for all \( x \) in the interval \([3, \infty)\).
**Domain of Continuity:**
Enter the domain of continuity below:
\[ \text{Domain of continuity: } [3, \infty) \]
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