supppose f:A->B and g:A->B,

then

(f+g)(x)=f(x)+g(x)

I don't understand how they can add f and g as though they were just scalars, I thought they were transitions from a to b.

so if I have the function f(x)=x^2 and g(x)=2x, then I know what f(x) and g(x) is, but I don't know what f and g by themselves mean.