(a) Given a function f, prove that g is even and h is odd, where g(x) = 1/2 [f (x) + f( x)] and h(x)

(a) Given a function f, prove that g is even and h is odd, where g(x) = 1/2 [f (x) + f(ˆ’ x)] and h(x) = 1/2 [f (x) ˆ’ f (ˆ’x)].
(b) Use the result of part (a) to prove that any function can be written as a sum of even and odd functions.
(c) Use the result of part (b) to write each function as a sum of even and odd functions.

f(x) = x? 2x + 1, k(x) =