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Math Help - Proving a function is wrong

  1. #1
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    Proving a function is wrong

    How do i prove that these two functions DO NOT exist?
    a) f(x) + g(y) = xy
    b) f(x)g(y) = x+ y

    Thanks so much!
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  2. #2
    MHF Contributor
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    Re: Proving a function is wrong

    if f(x) + g(y) = xy then f(x) + f(x) = x^2

    so the only possible candidate for f(x) is f(x) = 0.5 x^2.

    You can similarly reason for f(y) and hence end up with the (incorrect) equality 0.5x^2 + 0.5y^2 = xy, which you can easily show is false with a counter example.

    You try part (b).
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