I have to prove which of the following are subspaces of infinitely differentiable functions on R:

1) {f : f(0) = 0}

2) {f : f'(0) = 0}

3) {f : f(x) + f(-x) = 1}

4) {f : f(x) + f(-x) = f(0)}

I know that a subspace must be closed under addition and scalar multiplication, but I have no idea how to do this. How would you be able to test whether all of these are closed under addition and scalar multiplication?