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PROOF (a) Given a function f, prove that g(x) is even and h(x) is odd, where g(x) = (1)/(2)[f(x) f(-x)] and h(x) = (1)/(2)[f(x) - f(-x)]. (b) Use the result of part (a) to prove that any function can be written as a sum of even and odd functions. [Hint: Add the two equations in part (a).] (c) Use the result of part (b) to write each function as a sum of even and odd functions. f(x) = x^2 - 2x 1, k(x) = (1)/(x 1) | Numerade
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