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Math Help - Iterated function, please help!

  1. #1
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    Iterated function, please help!

    f_{o}(x)=\frac{1}{1-x}
    Let f_{r}(x)=f(f(f(...(f(x))...))
    Where there are r iterations of the function
    So f_{2}(x)=f(f(f(x)))
    Evaluate f_{2013}(\pi )
    Last edited by smokesalot; March 22nd 2013 at 04:13 AM.
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  2. #2
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    Re: Iterated function, please help!

    Hey smokesalot.

    Have you looked at finding a continued fraction form of your function?
    Thanks from smokesalot
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  3. #3
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    Re: Iterated function, please help!

    No, not really. The problem is that I don't completely understand the question
    Make that count 205 and help me here!
    Last edited by smokesalot; March 22nd 2013 at 04:42 AM.
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  4. #4
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    Re: Iterated function, please help!

    Quote Originally Posted by smokesalot View Post
    f_{o}(x)=\frac{1}{1-x}
    Let f_{r}(x)=f(f(f(...(f(x))...))
    Where there are r iterations of the function
    So f_{2}(x)=f(f(f(x)))
    Evaluate f_{2013}(\pi )
    This has a really nice simple answer.

    First calculate the explicit forms of f_1,~f_2,~\&~f_3.

    For example: f_1(x)=f_0(f_0(x))=\frac{x-1}{x}.
    Thanks from smokesalot
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  5. #5
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    Re: Iterated function, please help!

    Quote Originally Posted by Plato View Post
    This has a really nice simple answer.

    First calculate the explicit forms of f_1,~f_2,~\&~f_3.

    For example: f_1(x)=f_0(f_0(x))=\frac{x-1}{x}.
    f_{1}(x)=\frac{x-1}{x}

    f_{2}(x)=x

    f_{3}(x)=\frac{1}{1-x}

    f_{4}(x)=\frac{x-1}{x}

    Last edited by smokesalot; March 22nd 2013 at 07:25 AM.
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  6. #6
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    Re: Iterated function, please help!

    I am working on it now. I think I can do it!!!
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  7. #7
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    Re: Iterated function, please help!

    does that mean f_{0} = f_{2013}? then the answer is \frac{1}{1-\pi }
    Am I correct?
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  8. #8
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    Re: Iterated function, please help!

    Quote Originally Posted by smokesalot View Post
    does that mean f_{0} = f_{2013}? then the answer is \frac{1}{1-\pi }
    Am I correct?
    Exactly.

    f_N(x)=f_{mod(N,3)}(x)
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  9. #9
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    Re: Iterated function, please help!

    Thank you so much. I always get intimidated by this kind of questions but next time I will be brave and look for the pattern. There has to be one!
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