Thread: Sum and product of two even functions

I'm trying to prove that the sum and product of two even functions is even.

I know then that for f and g, which are even, f(A) = f(-A) and g(A) = g(-A).

Then f + g = f(A) + g(A) ....

I'm not sure exactly how to show this, or what I should get this equality to be, or if I even started it correctly. Any help on this?

Wait... I wanna show that (f+g)(x) = (f+g)(-x), right?

If that's the case, then this is VERY simple. Ugh!