Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q. 2 (page 669)

What is the definition of an odd function? An even function?

Short Answer

Expert verified

A function f is an odd function if f(−x)=−f(x) for all x in the domain off.

A function f is an even function if f(−x)=f(x)for all x in the domain of f.

Step by step solution

01

Step 1. Explain an odd function.

For a real-valued function f(x), when the output value of f(-x)is the same as the negative of f(x), for all values of x in the domain of f, the function is said to be an odd function.

An odd function should hold the following equation f(-x)=-f(x), for all values of x in the domain of the function f.

02

Step 2. Explain an even function.

For a real-valued function f(x), when the output value of f(-x)is the same as f(x), for all values of x in the domain of f, the function is said to be an even function. An even function should hold the following equation f(-x)=f(x), for all values of x in the domain of the function f.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let ∑k=0∞ akxkbe a power series in x with an interval of convergence[-2,2). What is the radius of convergence of the power series ∑k=0∞ ak(x−3)k? Justify your answer.

Why is it helpful to know the Maclaurin series for a few basic functions?

Prove that if the power series ∑k=0∞ akxkhas a positive and finite radius of convergence p, then the series ∑k=0∞ akx2khas a radius of convergence p.

Is it possible for a power series to have (0,∞)as its interval converge? Explain your answer.

In Exercises 49–56 find the Taylor series for the specified function and the given value of x0. Note: These are the same functions and values as in Exercises 41–48.

52.x,1
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free