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Math Help - continuos function

  1. #1
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    Question continuos function

    suppose f: [a,b] ->R is increasing
    and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

    I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
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  2. #2
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    Quote Originally Posted by dopi View Post
    suppose f: [a,b] ->R is increasing
    and for every Y in [f(a), f(b)], there is some x0 in [a,b] such that f(x0) = Y

    I want to show that f is a continious function but dont know how to go about this problem , can some one please help ..thanks
    If f(x) is strictly increasing and maps intervals into intervals. Then f(x) must be continous.

    Use the above fact to prove this partial conversve of the intermediate value theorem.
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