   Chapter 1.1, Problem 80E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If f and g are both even functions, is the product of fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd? Justify your answers.

To determine

To determine and justify: Whether the function fg is even if f and g are even; whether the function fg is odd if f and g are odd; whether the function fg is even or odd if f  is even and g is odd.

Explanation

Definition used:

If f(x)=f(x), the function f(x) is said to be an even function.

If f(x)f(x), the function f(x) is not an even function.

If f(x)=f(x), the function f(x) is said to be an odd function.

If f(x)f(x), the function f(x) is not an odd function.

Calculation:

If f and g are even functions, then by the definition, f(x)=f(x) and g(x)=g(x)

Recall the fact that, (fg)(x)=f(x)g(x) (1)

As f and g are even functions, substitute f(x)=f(x) and g(x)=g(x) in equation (1) as follows.

(fg)(x)=f(x)g(x)=f(x)g(x)=(fg)(x)

Therefore, fg is an even function as it satisfies the definition of an even function, (fg)(x)=(fg)(x).

If f and g are odd functions, then by definition, f(x)=f(x) and g(x)=g(x)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 516, evaluate the given quantity. log416

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Problem 45-51, solve each system of equations. 46.

Mathematical Applications for the Management, Life, and Social Sciences

#### In the graph at the right; limx2f(x)=. a) 2 b) 4 c) 0 d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Explain the role of voluntary participation in informed consent.

Research Methods for the Behavioral Sciences (MindTap Course List) 