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Math Help - Proof regarding 1-1 functions

  1. #1
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    Proof regarding 1-1 functions

    I want to disprove:
    If g of f is one-to-one, then g is one-to-one.

    Thanks for your help
    Last edited by Jhevon; November 15th 2009 at 04:04 PM.
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  2. #2
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    Quote Originally Posted by CoraGB View Post
    I have a similar problem, but in this case I want to disprove:
    If g of f is one-to-one, then g is one-to-one.

    Thanks for your help
    Take g(x)=x^2 and f(x)=e^x. The key is considering f such that g is injective restricted to the range of f, but not in all the domain of g. You can easily construct a los of these examples if you understand properly why this one works.
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