I have a homework question: Consider the maps: $$f : \mathbb{R}^2 \to \mathbb{R},\; (x,y) \mapsto x^2 +y^2$$ $$f : \mathbb{R} \to \mathbb{R},\; x \mapsto x^3$$ $$f : \mathbb{C} \to \mathbb{C},\; z \mapsto z^3$$ Determine the equivalence relation on the respective domains determined by $f$. Namely, explicitly describe equivalence classes from the map $f$.
I have no idea what it is asking, I know that equivalence relations can be used to divvy up a set, and I know that they are reflexive, symmetric, and transitive. But I do not know how to approach this.