a. Suppose that g is an even function of x and h is an odd function of x. Show that if g(x) + h(x) = 0 for all x then g(x) = 0 for all x and h(x) = 0 for all x.

b. Use the result in part (a) to show that if ƒ(x) = ƒ_E(x) + ƒ_O(x) is the sum of an even function ƒ_E(x) and an odd function ƒ_O(x), then ƒ_E(x) = (ƒ(x) + ƒ(-x))/2 and ƒ_O(x) = (ƒ(x) - ƒ(-x))/2.

c. What is the significance of the result in part (b)?