I have a function f(x) = y, as well as a set of pairs of constraints in the form of ranges of x and ranges of y. In practice, x and y are both vectors.
I'm trying to express this more mathematically, but not having much luck.
As an example, the set of constraints on x = {(-2, -1), (+1, +2)}, and the corresponding set of constraints on y = {(-10, -5), (+5, +10)}, such that:
for -2 < x < -1: -10 < f(x) < -5 (the first (x, y) constraint pair)
for +1 < x < +2: +5 < f(x) < +10 (the second (x, y) constraint pair)
I'll admit I'm not a mathematician but I need to be able to express this in some work I'm doing. I've been googling and haven't managed to make a lot of sense of how to do it. Basic set builder notation I can grasp, but this is getting a little beyond me. This post seems quite related but I'm struggling a bit - Convention of writing constraint sets.
Is anyone more knowledgeable than myself able to make any suggestions?