1. The problem statement, all variables and given/known data Let (G,*) be a group, and denote the inverse of an element x by x'. Show that f: G to G defined by f(x) = x' is a bijection, by explicitly writing down an inverse. Given x, y in G, what is f(x *y)? 2. Relevant equations 3. The attempt at a solution Okay, I think I'm just over thinking this... because it seems obvious that f is a bijection, since any function that has an inverse is bijective, and f obviously has an inverse where f-1(x')=x. And since x' and x are both in G, and G is a group then f-1 is well defined. But I keep having trouble with how to write proofs like this. Could someone help me out? Thanks!