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I wonder how to create a function based on the characteristics. suppose I have function $f$ and $g$ like this:

$f(x,g(x,y,z)) = y$ $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,$ $g(x,f(x,z),a) = z$

With $x,y,z,a$ are the parameters. Are there "algorithm" to "generate" arbitrary function which appropriate to that functions (f and g)?$\,\,\,$ or I should use brute forces / try and error to do that? what mathematics branch to study that?

smftr
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  • Do you know anything else about $f,g$ or how they're related? – John Sep 29 '14 at 16:01
  • hi @John , the example was just arbitrary nonsense which out from my mind. I just want to know are there formal ways to solve that with "step by step" which agree with all possibility of characteristic functions. – smftr Sep 30 '14 at 04:09

1 Answers1

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One solution that came to my mind is $f(x,y)=x+y$ and $g(x,y,z)=y-x$. Besides guessing the functions, you could try guessing the form of the functions. For example, if you assume the functions are linear, you can try to solve for the coefficients. A good guess of the form depends on the context, if the functions are supposed to be related to something. Do you have any reason to assume that the functions have some special properties?

Joonas Ilmavirta
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