Okay, so the question I am working on is, "Suppose that A is a nonempty set, and $f$ is a function that has A as its domain. Let R be the relation on A consisting of all ordered pairs $(x, y)$ such that $f(x)=f(y)$.
a)Show that R is an equivalence relation on A.
b)What are the equivalence classes of R?"
I was able to part a, but I am not certain how to answer part b. I know that the domain is the set A, but what is the range? And when you say that $f(x)=f(y)$, does that mean that a function is equal to its inverse? Like for instance, $\Large y=\frac{1}{x}$