Question: 3. Let V be the vector space of functions / : R + R. Let Wj be the subset of even functions, and Wa be

3. Let V be the vector space of functions / : R + R. Let Wj be the subset of even functions, and Wa be the subset of odd functions. (a) (4 points) Show that W, and Wa is are subspaces of V. (b) (10 points) Show that V = WOW2. (Hint: Let fi(x) = 5(f(x) + f(-r)) and 2(3) = .5(/(x) - /(-1)). (c) (4 points) Find the projection of f(x) = 2e" - e" + 3r + 1 onto W, along W2

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