(a) Show that the set of even functions, f(-x) = f(x) is a subspace of the vector space of all functions .F(R).
(b) Show that the set of odd functions g(- x) = - g(x) forms a complementary subspace, as defined in Exercise 2.2.24.
(c) Explain why every function can be uniquely written as the sum of an even function and an odd function.