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used only for functions based on gamma, not functions with some obscure relation to gamma
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Proving injectivity of a multivariable function
Let $I$ denote the interval $(0,\infty)$, we define the function $f:I^2\to I^2$ by,
$$f(x,y)=\left({\Gamma(4x+y)\Gamma(y)\over {\Gamma(2x+y)}^2},{\Gamma(4x+y)\Gamma(2x+y)\over {\Gamma(3x+y)}^2}\right) …