Chapter 1.1, Problem 80E

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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 *f* and *g* are even; whether the function *f* and *g* are odd; whether the function *f* is even and *g* is odd.

Explanation

**Definition used:**

If

If

If

If

**Calculation:**

If *f* and *g* are even functions, then by the definition,

Recall the fact that,

As *f* and *g* are even functions, substitute

Therefore, *fg* is an even function as it satisfies the definition of an even function,

If *f* and *g* are odd functions, then by definition,

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