Vector space functions

Question

Problem:

Vector space functions

Let V be the vector space of all functions ƒ : 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  = { ƒ∈V| ƒ(0) = 0}

B. W = { ƒ∈V| ƒ(X) = K₁ + K₂ sin x for some k₁,k₂∈ℜ}