Assume that p is a function that is defined for all x (a) Prove that if is defined by (x) p(x) p(x) then is even (b) Prove that if g is defined by g(x) p(x) p(x) then g is odd

Question: Assume that p is a function that is defined for all x. (a) Prove that if is defined by (x) = p(x) + p(x)

Assume that p is a function that is defined for all x.
(a) Prove that if ƒ is defined by ƒ(x) = p(x) + p(−x) then ƒ is even.
(b) Prove that if g is defined by g(x) = p(x) − p(−x) then g is odd.

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