Even and odd proof

[quasar987]

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.

 

[Physics Monkey]

Try looking at f(-x) and relating it to p(x) and i(x). Do you notice anything?

 

[quasar987]

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:

 

[Hurkyl]

f(x) = p+i and hence f(-x) = p(x)-i(x), but that's as far as that goes.

No it's not.

 

[quasar987]

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