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Math Help - a question about function?

  1. #1
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    a question about function?

    Please show me some continuous function with a domain in the closed interval [0,1] and its range is also [0,1].
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  2. #2
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    The identity map

    f:[0,1]\to [0,1]
    f(x)=x

    is a continuous function with domain and range [0,1]
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  3. #3
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    Quote Originally Posted by boxxkutexx View Post
    Please show me some continuous function with a domain in the closed interval [0,1] and its range is also [0,1].
    Suppose that n\in \mathbb{Z}^+, a positive integer.
    Then f(x)=x^n will work.
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  4. #4
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    thank u so much. it seems very simple.
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