:. Let V = C" (R, R) be the vector space of real valued continuous functions defined on R. (a) Prove that V is infinite dimensional.(h) (b) Prove or disprove

that the set W := {f € V : S(x)| < 3 for all r ER} is a subspace ofV. (c) Give an example of a two dimensional subspace, UCV. Give a basis (with proof) for U and find an isomorphism between U and R².