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Some context, I was trying to derive something and stumbled upon f(x,y)f(y,x)=1, when x and y does not equal 0. Could someone suggest some tricks or books that I could apply to these types of questions? By the way, I'm trying to solve for f(x,y)and I'm aware that one solution could be f(x,y)=x/y, but I would like to know how to derive it.

Thank you.

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There are infinitely many functions satisfying this property. You can start with any function $f(x,y)$ defined for $\{(x,y): x \leq y\}$ which does not vanish at any point and define $f(y,x)=\frac 1 {f(x,y)}$ for $x >y$.

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  • $\begingroup$ Would there be a book you could refer me to? Specifically, any one that deals with functionals with more than one input? $\endgroup$ – BonInSossusvlei Jul 5 at 23:43

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