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?