3. Let V denote the vector space of all functions f : R → R, equipped with addition + : V x V → V defined via (f+g)(x) = f(x) + g(x), x = R, and scalar multiplication : Rx V → V defined via (X. f)(x) = f(x), xER". Now let W = {f: R→ R: f(x) = ax + b for some a, b = R}, i.e. the space of all linear functions R → R. (a) Show that W is a subspace of V. (You may assume that V is a vector space). (b) Find a basis for W. You should prove that it is indeed a basis.

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