Hi, I've done some exercises to determine wheter a subset is a subspace, but I don't know how to do the ones with functions, like the following:

Determine wheter the following subset is a subspace of the vector space of all the functions f(x), x ∈ R.

G={acosx+bsinx: a, b ∈ R}

So, I have to check that G satisfies the additive identity, the closed under addition and closed under escalar properties.

I think the first condition is satisfied, right? How do I check if the other two are satisfied?