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If f(x,y)+f(y,x)=0 for any x,y, is it true that f(x,y)=g(x)-g(y)

  1. Apr 29, 2012 #1
    If f(x,y)+f(y,x)=0 for any x,y, is it true that f(x,y) can always be written as g(x)-g(y)?

    If so, how to prove it?
     
  2. jcsd
  3. Apr 29, 2012 #2
    No. For example yg(x)-xg(y) also satisfies the relation.
    Regards.
     
  4. Apr 29, 2012 #3
    Thanks
     
  5. Apr 30, 2012 #4
    In general f(x,y)=g(x,y)-g(y,x) obviously.
     
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