Even and odd proof

I'm puzzled by this question: Show that for all function f:R-->R. there exists an even function p and an odd function i such that f(x) = p(x) + i(x) forall x in R.

I got nothing.

 

But there is nothing to look at. f(-x) = ..........................?

The only thing would be SUPPOSING the result of the thorem is true, then it would implies that there exist p and i such that f(x) = p+i and hence f(-x) = p(x)-i(x), but that's as far as that goes. :grumpy:

 

Oh I see. That was very insightful Hurkyl. :tongue: