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## Homework Statement

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.

## Homework Equations

I think I need to show that (f+g)(x) = f(x) + g(x) and that (rf)(x) = rf(x)

## 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).