# Proving a function is onto

1. Nov 10, 2012

### gottfried

1. The problem statement, all variables and given/known data

Let G be a group and define λg:G→G to be λg(x)=g.x , x$\in$G.

Show that λg is onto and one-to-one.

3. The attempt at a solution
Suppose g.x=g.x' g-1.g.x=g-1.g.x' which means x=x'.

How should I show that the function is onto?

2. Nov 10, 2012

### HallsofIvy

Staff Emeritus
If y is any member of G, then $\lambda(g^{-1}y)= y$