Homework Help is Here – Start Your Trial Now!
Math
Algebra
If f(x) is an even function, which function must also be even? (1) f(x – 2) (2) f(x) + 3 (3) fl(x + 1) (4) f(x + 1) + 3

If f(x) is an even function, which function must also be even? (1) f(x – 2) (2) f(x) + 3 (3) fl(x + 1) (4) f(x + 1) + 3

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question
### Question 7: Even Functions If \( f(x) \) is an even function, which function must also be even? Options: 1. \( f(x - 2) \) 2. \( f(x) + 3 \) 3. \( f(x + 1) \) 4. \( f(x + 1) + 3 \) **Explanation:** An even function \( f(x) \) is defined such that \( f(x) = f(-x) \) for all \( x \) in the domain of \( f \). This property can help us determine which modifications to \( f(x) \) preserve its even nature. 1. **\( f(x - 2) \)**: - To check if \( f(x - 2) \) is even, we substitute \( -x \) and compare: \( f(x - 2) \) and \( f(-x - 2) \). Since \( x - 2 \neq -x - 2 \), \( f(x - 2) \) is not necessarily even. 2. **\( f(x) + 3 \)**: - Adding a constant to \( f(x) \) does not change the symmetry of \( f(x) \). Therefore, if \( f(x) \) is even, \( f(x) + 3 \) remains even. 3. **\( f(x + 1) \)**: - To check if \( f(x + 1) \) is even, we substitute \( -x \) and compare: \( f(x + 1) \) and \( f(-x + 1) \). Since \( x + 1 \neq -x + 1 \), \( f(x + 1) \) is not necessarily even. 4. **\( f(x + 1) + 3 \)**: - Similar to option 3, since \( f(x + 1) \) is not necessarily even, adding a constant does not change this. Therefore, \( f(x + 1) + 3 \) is not necessarily even. **Conclusion:** The function that must also be even if \( f(x) \) is an even function is: \( \boxed{2} \ f(x) + 3 \)
Transcribed Image Text:### Question 7: Even Functions If \( f(x) \) is an even function, which function must also be even? Options: 1. \( f(x - 2) \) 2. \( f(x) + 3 \) 3. \( f(x + 1) \) 4. \( f(x + 1) + 3 \) **Explanation:** An even function \( f(x) \) is defined such that \( f(x) = f(-x) \) for all \( x \) in the domain of \( f \). This property can help us determine which modifications to \( f(x) \) preserve its even nature. 1. **\( f(x - 2) \)**: - To check if \( f(x - 2) \) is even, we substitute \( -x \) and compare: \( f(x - 2) \) and \( f(-x - 2) \). Since \( x - 2 \neq -x - 2 \), \( f(x - 2) \) is not necessarily even. 2. **\( f(x) + 3 \)**: - Adding a constant to \( f(x) \) does not change the symmetry of \( f(x) \). Therefore, if \( f(x) \) is even, \( f(x) + 3 \) remains even. 3. **\( f(x + 1) \)**: - To check if \( f(x + 1) \) is even, we substitute \( -x \) and compare: \( f(x + 1) \) and \( f(-x + 1) \). Since \( x + 1 \neq -x + 1 \), \( f(x + 1) \) is not necessarily even. 4. **\( f(x + 1) + 3 \)**: - Similar to option 3, since \( f(x + 1) \) is not necessarily even, adding a constant does not change this. Therefore, \( f(x + 1) + 3 \) is not necessarily even. **Conclusion:** The function that must also be even if \( f(x) \) is an even function is: \( \boxed{2} \ f(x) + 3 \)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Limits and Continuity
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS