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 (x) E (x) O (x) is the sum of an even function E (x) and an odd function O (x), then E (x) ((x) ( x)) 2 and O (x) ((x) ( x)) 2 c What is the significance of the result in part (b)

Question: 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) =

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)?

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a Since gx is even gx gx And since hx is odd hx hx Thus we have gx hx 0 gx hx 0 taking the ... View full answer

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