Problem on vector space functions

Question

Assignment:

Let V be the vector space of all functions F : R → R. Determine whether the following subsets of V form subspaces of V. Give reasons, ie, prove or disprove that the subset is a subspace.

a) U = {f ∈ V | f(0) = 0
b) W = {f ∈ V | f(x) = k₁ + k₂ sin x for some k₁, k₂ ∈ R

Provide complete and step by step solution for the question and show calculations and use formulas.