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Math Help - A couple more questions involving functions

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Janu42 View Post
    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!
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