Question: (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

(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.

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a If fx fx x x then cf dx cf x dx cf x dx cf dx for any c d R and hence it is a subspace b ... View full answer

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