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Math Help - Use algebra to identify the points of the 2-cycle?

  1. #1
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    Exclamation Use algebra to identify the points of the 2-cycle?

    f(x) = 9/x + x/2 - c

    c ≤ 3.5

    I'm pretty sure you just have to solve f(f(x))-x = 0. But, that doesn't seem possible...
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Mitchell View Post
    f(x) = 9/x + x/2 - c

    c ≤ 3.5

    I'm pretty sure you just have to solve f(f(x))-x = 0. But, that doesn't seem possible...
    Why not? f(f(x))= f(9/x+ x/2- c)= 9/(9/x+ x/2+ c)+ (9/x+ x/2+ c)/2- c= 9x/(9- x^2+ cx)+ 9/(2x)+ x/4+ c/2.

    So you want to solve
    \frac{9x}{9- x^2+ cx}+ \frac{9}{2x}+ x/4+ c/2- x= 0
    Difficult perhaps but possible.
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