# Math Help - A couple more questions involving functions

1. ## 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?

2. 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 $f$ is one-to-one you need to argue if $f(x) = f(y)$ then $x=y$. To show it is onto you need to show that for any $y\in G$ we can solve the equation $f(x) = y$ for $x$. Post what you did!