If you know a,b,m,n1,n2,n3, and use sufficient points, you may be able to get an interpolated approximation.

In general, one can fit many such curves through a finite set of points. http://math.stackexchange.com/questions/65970/can-a-function...

A question originally asked by Leibniz to determine the measure of usefulness of a law. https://plus.maths.org/content/omega-and-why-maths-has-no-to....

If you don't have the 6 parameters, good luck. A unique inverse is defined only for injective functions.