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Math Help - interesting question

  1. #1
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    interesting question

    is there a continuous real-valued function on R which takes all its values exactly twice?
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  2. #2
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    Hello, zhupolongjoe!

    I hope I didn't misread the problem . . .


    Is there a continuous real-valued function on R
    which takes all its values exactly twice?

    How about: . f(x) \:=\:x^2

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, zhupolongjoe!

    I hope I didn't misread the problem . . .



    How about: . f(x) \:=\:x^2

    problem is ... f(x) = 0 only once
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  4. #4
    MHF Contributor Drexel28's Avatar
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    There is none. Want to see a proof?
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  5. #5
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    If you've got time...or even just the idea of the proof.
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by zhupolongjoe View Post
    If you've got time...or even just the idea of the proof.
    Here is a similar proof. See if you can understand it, and if you can see if you can generalize to your question. If you have any trouble report back.

    You may need to scroll down a little.
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