# Thread: Help w/ some proofs even/odd functions

1. ## Help w/ some proofs even/odd functions

Hey guys, I was hoping for some help on a problem. I havent dont this kind of stuff in 6/7 years. Here it is...

A function f(x) is defined as even if f(−x) = f(x) for all x. A function f(x) is defined as odd if f(−x) = −f(x) for all x. Prove, using other than geometrical arguments, the following properties of even and odd functions:
(a) The product of two even functions is even.
(b) The product of an even and an odd function is odd.
(c) The product of two odd functions is even.

2. Originally Posted by Marv
Hey guys, I was hoping for some help on a problem. I havent dont this kind of stuff in 6/7 years. Here it is...

A function f(x) is defined as even if f(−x) = f(x) for all x. A function f(x) is defined as odd if f(−x) = −f(x) for all x. Prove, using other than geometrical arguments, the following properties of even and odd functions:
(a) The product of two even functions is even.
(b) The product of an even and an odd function is odd.
(c) The product of two odd functions is even.
a)Let f(x) and g(x) both be even functions.
Define h(x) = f(x)g(x).
We wish to show that h(-x) = h(x).
Well, h(-x) = f(-x)g(-x) and f(-x) = f(x), g(-x) = g(x)
So h(-x) = f(-x)g(-x) = f(x)g(x) = h(x)
Thus h(-x) = h(x).

The other two proofs are very similar.

-Dan

3. gracias...i got it