1. The problem statement, all variables and given/known data Let S be a set and V a vector space over the field k. Show that the set of functions f: S --> k, under function addition and multiplication by a constant is a vector space. 2. Relevant equations I think I need to show that (f+g)(x) = f(x) + g(x) and that (rf)(x) = rf(x) 3. The attempt at a solution Are the above conditions true because both functions f and g for this particular case give you k and (k1 + k2) = k1 + k2 and rk = rk. I just don't understand how to show it. Or do I just literally write (f+g)(x) = f(x) + g(x) and that (rf)(x) = rf(x).