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Homework Help: Even and odd proof

  1. Sep 15, 2005 #1

    quasar987

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    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.
     
    quasar987, Sep 15, 2005
  2. jcsd
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  3. Sep 15, 2005 #2

    Physics Monkey

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    Try looking at f(-x) and relating it to p(x) and i(x). Do you notice anything?
     
    Physics Monkey, Sep 15, 2005
  4. Sep 15, 2005 #3

    quasar987

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    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:
     
    quasar987, Sep 15, 2005
  5. Sep 15, 2005 #4

    Hurkyl

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    No it's not.
     
    Hurkyl, Sep 15, 2005
  6. Sep 15, 2005 #5

    quasar987

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    Oh I see. That was very insightful Hurkyl. :tongue:
     
    quasar987, Sep 15, 2005
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