# When you multiply two odd or two even functions, what type of function will you get?

##### 1 Answer

#### Answer:

Always even (unless its domain is empty).

#### Explanation:

**Odd times odd**

Suppose

By definition:

#f(-x) = -f(x)# and#g(-x) = -g(x)# for all#x#

So:

#h(-x) = f(-x)g(-x) = (-f(x))(-g(x)) = f(x)g(x)#

#= h(x)# for all#x#

So

**Even times even**

Now suppose that

By definition:

#f(-x) = f(x)# and#g(-x) = g(x)# for all#x#

So:

#h(-x) = f(-x)g(-x) = f(x)g(x) = h(x)# for all#x#

So

**Exception**

If the domains of

For example:

Let

Then the domain of

The domain of