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Math Help - Existence of a function

  1. #1
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    Existence of a function

    Do there exist functions f: R --> R such that

    f(x) - f(-x) = x^2 for all x \epsilon  R?

    I've a hunch it's no, as any squared term would be the same under x and -x, but I'm not sure how to provide a formal proof.
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  2. #2
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    Quote Originally Posted by h2osprey View Post
    Do there exist functions f: R --> R such that
    f(x) - f(-x) = x^2 for all x \epsilon  R?
    I've a hunch it's no, as any squared term would be the same under x and -x, but I'm not sure how to provide a formal proof.
    If g is any function on \mathbb{R} and h(x)=g(x)-g(-x) can you show that h is an odd function?
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  3. #3
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    Ah yes of course. Thanks!
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