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Math Help - doubt on statements concerning the behavior of functions

  1. #1
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    doubt on statements concerning the behavior of functions

    which of the following statements is true?
    1) f invertible then f strictly monotone
    2) f strictly monotonic then f invertible
    3) f strictly increasing then f unbounded from above
    4) f strictly decreasung then f has a global minimum
    i would say the first but i'm not convinced, may smone explain me what and why?
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  2. #2
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    Quote Originally Posted by Aglaia View Post
    1) f invertible then f strictly monotone
    Yes, assume it is not then there are two points such that
    f(x)=f(y) thus, f is not one to one function.

    2) f strictly monotonic then f invertible
    No, in addition f needs to be countinous
    f strictly increasing then f unbounded from above
    Consdier, f=x^3
    4) f strictly decreasung then f has a global minimum
    No
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  3. #3
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    thank u!
    Last edited by ThePerfectHacker; September 27th 2006 at 09:10 AM.
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