Prove that the sum of two odd functions is odd.

Odd function: f (-x) = - f (x)

Let two odd functions be f (x) and g (x)

Let k (x) = f (x) + g (x)

Then k (-x) = f (-x) + g (-x) = - (f (x) + g (x)) = - k (x)

So k (x) is odd too.