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.