Okay, I think I've figured it out

First: Show that each of the equivalence classes are distinct. Because g(x) is strictly increasing, then it must be the case that , then so must the sequence x, g(x), g(g(x)) be strictly increasing, meaning that , which means that

Hence, we only need to look at the values of f(x) within the domain of (0,2012). The answer is then just