Find the domain of the following function. Do not use a graphing calculator f(x) = 1 x2 - 5x - 6 The domain is (Type your answer in interval notation.) ***
Find the domain of the following function. Do not use a graphing calculator f(x) = 1 x2 - 5x - 6 The domain is (Type your answer in interval notation.) ***
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,...
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![**Finding the Domain of a Rational Function**
**Problem Statement**
Find the domain of the following function. Do not use a graphing calculator.
**Function**
\[ f(x) = \frac{1}{x^2 - 5x - 6} \]
**Instructions**
Determine the domain of the function by identifying the values of \( x \) for which the denominator is not equal to zero. Provide your answer in interval notation.
**Domain Answer Box**
\[ \text{The domain is } \_\_\_\_\_ \]
*(Type your answer in interval notation.)*
**Tools and Resources**
- View an example
- Get more help
**User Interface Elements**
- "Clear all" button
- "Skill builder" button
Explore the steps to find the domain:
1. Set the denominator equal to zero: \( x^2 - 5x - 6 = 0 \).
2. Solve for \( x \) where the function is undefined.
3. Exclude these \( x \)-values from the real number set to determine the domain.
4. Express the domain using interval notation.
**Solution Outline**
1. Factor the quadratic equation \( x^2 - 5x - 6 = 0 \) to find the critical points where the function is undefined.
2. Identify the intervals where the function is defined.
3. Write these intervals in interval notation as the domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c22293a-3ae6-4ac2-9c37-c12acd82a0e8%2Fd921dc41-14c9-4b51-8995-2fa7126921d8%2Fkejmqqa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Domain of a Rational Function**
**Problem Statement**
Find the domain of the following function. Do not use a graphing calculator.
**Function**
\[ f(x) = \frac{1}{x^2 - 5x - 6} \]
**Instructions**
Determine the domain of the function by identifying the values of \( x \) for which the denominator is not equal to zero. Provide your answer in interval notation.
**Domain Answer Box**
\[ \text{The domain is } \_\_\_\_\_ \]
*(Type your answer in interval notation.)*
**Tools and Resources**
- View an example
- Get more help
**User Interface Elements**
- "Clear all" button
- "Skill builder" button
Explore the steps to find the domain:
1. Set the denominator equal to zero: \( x^2 - 5x - 6 = 0 \).
2. Solve for \( x \) where the function is undefined.
3. Exclude these \( x \)-values from the real number set to determine the domain.
4. Express the domain using interval notation.
**Solution Outline**
1. Factor the quadratic equation \( x^2 - 5x - 6 = 0 \) to find the critical points where the function is undefined.
2. Identify the intervals where the function is defined.
3. Write these intervals in interval notation as the domain.
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