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

  • #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?
 

Answers and Replies

  • #2
1,225
75
No. For example yg(x)-xg(y) also satisfies the relation.
Regards.
 
  • #4
1,225
75
In general f(x,y)=g(x,y)-g(y,x) obviously.
 

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