Show that if a function is defined on an interval symmetric about the origin (so that

Show that if a function ƒ is defined on an interval symmetric about the origin (so that ƒ is defined at -x whenever it is defined at x), then

Then show that (ƒ(x) + ƒ(-x))/2 is even and that (ƒ(x) - ƒ(-x))/2 is odd.

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f(x) = f(x) + f(-x) 2 + f(x) = f(-x) 2 (1)