Given the equivalence relation R on the set of all functions

Given the equivalence relation R on the set of all functions from Z to Z.

R = { (f,g) I f(x) - g(x) = C, fpr some C is a element of Z, every x is element of Z}

What is the equivalence class for f(x) = x² ?

Explain the steps

Solution

f(x) -g(x) = C where C is an integer and x is also an integer

If f(x) =x²

define g(x) = (x-1)²

Then f(x) -g(x) = 2x-1 is again an integer

Hence this is an example of equivalance class for f(x)