Symmetric and Antisymmetric Parts

Any function f(x) can be split into a symmetric part: g(x) = (f(x) + f(-x))/2 and an antisymmetric part: h(x) = (f(x)-f(-x))/2.
Verify that these satisfy:
f(x) = g(x) + h(x)
g(x) = g(-x)
h(x) = -h(-x)

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f(x)

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