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Math Help - Suitable function H(H(x))=H(x)

  1. #1
    Junior Member
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    Oct 2010
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    Suitable function H(H(x))=H(x)

    Hi just a question from the book I'm a bit puzzled with, probably fairly basic but I am very tired and can't make any sense of it :/

    Find a suitable function H such that H(H(x))=H(x), and H(1)=36, H(2)=\frac{\pi}{3}, H(13)=47, H(36)=36, H(\frac{\pi}{3})=\frac{\pi}{3}, H(47)=47

    Hint: Don't try to solve for H(H(x))=H(x), the further conditions are to guide you to a suitable H

    I understand how they go together as in:

    H(H(1))=H(1)
    H(H(2))=H(2)
    H(H(13)=H(13)

    But I'm not sure of the form the function H will take??

    Thank you!
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  2. #2
    Senior Member
    Joined
    Oct 2009
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    The important values of x are the ones where H(x) = x. For such an x, if y is such that H(y) = x then clearly H(H(y)) = H(y). Think along the lines of partitioning the reals.
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