Find the domain of the function. 10 x-7 f(x)= What is the domain of f? OA. (-0,7) or (7,00) OB. (-∞0,0) or (0,7) or (7,00) OC. (-∞,0) or (0,00) OD. (-00,00)
Find the domain of the function. 10 x-7 f(x)= What is the domain of f? OA. (-0,7) or (7,00) OB. (-∞0,0) or (0,7) or (7,00) OC. (-∞,0) or (0,00) OD. (-00,00)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Finding the Domain of the Function**
**Function:**
\[ f(x) = \frac{10}{x - 7} \]
**Problem:**
Identify the domain of \( f \).
**Options:**
- **A.** \( (-\infty, 7) \) or \( (7, \infty) \)
- **B.** \( (-\infty, 0) \) or \( (0, 7) \) or \( (7, \infty) \)
- **C.** \( (-\infty, 0) \) or \( (0, \infty) \)
- **D.** \( (-\infty, \infty) \)
**Explanation:**
The function \( f(x) = \frac{10}{x - 7} \) is undefined when the denominator is zero. Thus, \( x - 7 = 0 \) implies \( x = 7 \). Therefore, the function is undefined at \( x = 7 \).
The domain of \( f \) consists of all real numbers except \( x = 7 \). Hence, the correct domain is \( (-\infty, 7) \cup (7, \infty) \).
- The correct choice is **A.** \( (-\infty, 7) \) or \( (7, \infty) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F259dd315-7abd-4762-908b-82a0c799e6cc%2F1af55e0b-7029-4a92-bc50-20d5978d83c8%2F6y1vrbo_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Domain of the Function**
**Function:**
\[ f(x) = \frac{10}{x - 7} \]
**Problem:**
Identify the domain of \( f \).
**Options:**
- **A.** \( (-\infty, 7) \) or \( (7, \infty) \)
- **B.** \( (-\infty, 0) \) or \( (0, 7) \) or \( (7, \infty) \)
- **C.** \( (-\infty, 0) \) or \( (0, \infty) \)
- **D.** \( (-\infty, \infty) \)
**Explanation:**
The function \( f(x) = \frac{10}{x - 7} \) is undefined when the denominator is zero. Thus, \( x - 7 = 0 \) implies \( x = 7 \). Therefore, the function is undefined at \( x = 7 \).
The domain of \( f \) consists of all real numbers except \( x = 7 \). Hence, the correct domain is \( (-\infty, 7) \cup (7, \infty) \).
- The correct choice is **A.** \( (-\infty, 7) \) or \( (7, \infty) \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education