There is a function $f(x)$ obtained from fit to experimental data. The shape of the function is not fixed yet, the data can be fitted to various curves, e.g. to exponential or polynomial. I need to choose this function so that when $x$ is substituted by $a b - x$, one of the following decompositions was valid: $$f(a b - x) \approx f_1(a, x) f_2(b, x)$$ or $$f(x) f(a b - x) \approx f_1(a, x) f_2(b, x).$$ I guess the the question is related to http://en.wikipedia.org/wiki/Functional_decomposition, but I'm not sure if decomposition into a product is possible in my case and how to proceed.
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