Determine the subsets of v form subspaces

Question

Problem:

Algebra: Vector Spaces

Let V be the vector space of all functions f: R →R. Determine whether the following subsets of V form subspaces.

a) U = {f belongs to V | f(0) = 0}

b) W = {f belongs to V | f(x) = k₁ + k₂ sinx for some k₁,k₂ are reals}.