- #1

Gale

- 676

- 2

**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)?

## Homework Equations

## 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!