If f(x) and g(x) are both even functions, is f + g even? If f(x) and g(x) are both odd functions, is f + g odd? What if f(x) is even and g(x) is odd?
Now intuitively I get that for the first one, the resulting answer will be EVEN
For second one it will be ODD
And for the last one it will be Neither.
But I don't know how to justify that... it just came to me intuitively, Can someone show me a way through al-gebra to prove my claim.