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Math Help - Find simple expression for f28

  1. #1
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    Find simple expression for f28

    For the functions
    f1(x)=(2x-1)/(x+1)
    f(n+1)(x)=f1(fn(x)) for n>=1
    it can be shown that f35=f5.Find the simple expression for f28.
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  2. #2
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    Quote Originally Posted by chris86 View Post
    For the functions
    f1(x)=(2x-1)/(x+1)
    f(n+1)(x)=f1(fn(x)) for n>=1
    it can be shown that f35=f5.Find the simple expression for f28.
    If f_{35} = f_5 then f_1 composed with itself 35 times is the same as f_1 composed with itself 5 times. So f_1 composed with itself 30 times must be the identity function. Therefore f_{28} = f_{-2}. So find the inverse function of f_1 and take its composition with itself. That will give you f_{-2}.
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