How to combine two pairs of arrays (input and output) into one that is the union between both inputs but keeps both outputs referenced to the same data of its input before the union?

Suppose that I have these two matrix (each one a pair of in-output data): [x f(x)] and [y f(y)]. The array x and y measure the same variable but they are displaced by an offset. The objective is to unite both input variables x and y into a single array (xUy - x union y) but keep its outputs f(x) and f(y) referenced to the same points that they were with x and y.

Is there a function to it? Can I do it through the 'union' command?

[the cyclist]

How are the data stored? Can you give a small example of inputs and expected output?

[Rik]

Can't you just concatenate them and use unique to get the unique rows?