Thread: A couple more questions involving functions

1. Let G be a group and let a be in G. Define a function f: G --> G by f(x) = axa^-1 for all x in G. Is f one-to-one? Is it onto?

2. Let G be a group, and let f(x) = x^-1 for all x in G. Is f a function from G to G? If so, is it one-to-one? Is it onto?

Originally Posted by Janu42

1. Let G be a group and let a be in G. Define a function f: G --> G by f(x) = axa^-1 for all x in G. Is f one-to-one? Is it onto?

2. Let G be a group, and let f(x) = x^-1 for all x in G. Is f a function from G to G? If so, is it one-to-one? Is it onto?

In both of these problems this is what you need to do. To show it is is one-to-one you need to argue if then . To show it is onto you need to show that for any we can solve the equation for . Post what you did!