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Homework Help: Stuck on this function

  1. Sep 27, 2005 #1

    Jeff Ford

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    I'm going through the review section of the Stewart Calculus text and I'm stuck on this problem.

    Given
    [itex]
    f_0(x) = x^2
    [/itex]
    and
    [itex]
    f_0(f_n(x)) = f_{n+1}(x) , n = 0,1,2...
    [/itex]
    how do you solve for
    [itex]
    f_n(x)
    [/itex]
     
    Last edited: Sep 27, 2005
    Jeff Ford, Sep 27, 2005
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  3. Sep 27, 2005 #2

    Jeff Ford

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    The only place I can think to start is making [itex] (f_n(x))^2 = f_{n+1}(x) [/itex], but that's as far as I got
     
    Jeff Ford, Sep 27, 2005
  4. Sep 27, 2005 #3

    VietDao29

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    Homework Helper

    Now, f1(x) = f0(f0(x)) = f0(x2) = x4
    f2(x) = f0(f1(x)) = f0(x4) = x8
    f3(x) = f0(f2(x)) = ...
    f4(x) = f0(f3(x)) = ...
    So what's fn(x)?
    Can you go from here?
    Viet Dao,
     
    VietDao29, Sep 27, 2005
  5. Sep 27, 2005 #4

    Jeff Ford

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    From that I get [itex] f_n(x) = x^{2^{n+1}} [/itex] but that doesn't work for [itex] f_0(x) = x^2 [/itex]. That's the same answer the book has, so maybe I wrote the requirements down wrong. I'll have to check when I get home if this had to work for 0.
     
    Jeff Ford, Sep 27, 2005
  6. Sep 27, 2005 #5

    Jeff Ford

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    Yes it does. Never mind.

    Thanks Viet Dao!
     
    Jeff Ford, Sep 27, 2005
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