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Math Help - Inverse functions

  1. #1
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    Inverse functions

    I've been set a question and I just want to verify I have understood it and would like a few pointers on solving it.

    Given R=C[0,1]
    -Firstly this is any function that is continuous on the domain [0,1] ?
    I.e. f:[0,1] -> Reals

    -The group of units is all continuous functions that are invertible on [0,1].
    By my understanding: those that have no asymptotes (continuity), and no roots (invertibility) on [0,1].

    Is there any way to classify these functions more rigourously?

    Thanks
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by mrmango View Post
    I've been set a question and I just want to verify I have understood it and would like a few pointers on solving it.

    Given R=C[0,1]
    -Firstly this is any function that is continuous on the domain [0,1] ?
    I.e. f:[0,1] -> Reals
    Well, \mathcal{C}[E],\text{ }E\subseteq \mathbb{R} is the set of all bounded functions f:E\mapsto\mathbb{R} continuiously. In your case you just lucked out that continuity implies boundedness.

    -The group of units is all continuous functions that are invertible on [0,1].
    By my understanding: those that have no asymptotes (continuity), and no roots (invertibility) on [0,1].

    Is there any way to classify these functions more rigourously?

    Thanks
    I'm not sure what you mean here? You can turn \mathcal{C}[0,1] into a ring?
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  3. #3
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    Thanks for your reply,

    Im pretty sure it is a ring, but correct me if i'm wrong

    Thanks again
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by mrmango View Post
    Thanks for your reply,

    Im pretty sure it is a ring, but correct me if i'm wrong

    Thanks again
    It is a ring.
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