Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Question on composition of functions

  1. #1
    Jan 2013

    Question on composition of functions


    For some m = p/q in the rational numbers consider the map f_m = [0,1) -> [0,1) defined by f_m(x) = (x + m) mod 1 for all x element of [0,1).

    a) Show that f(superscript q, subscript m) = Identity on [0,1)

    (my comment): This refers to the composition of f_m, q times, where q is the denominator of the rational number.

    b) Now suppose we consider m in the irrationals, what happens to the iterates f(superscript n, subscript m)(x) for any point x as n gets larger?

    For (a) I have done several "examples" to verify to myself this works. However I am not sure how to go about constructing a proof. My main problem stems from the uncertainty in representing f(superscript q, subscript m).

    I know it is just (f_m o f_m o f_m ... o f_m) q times, but how do you generalize something like that?

    (b) I'm not sure on how to proceed. Does it also happen to approach the identity? (just a guess)

    Edit: I got (a) just need help on (b).
    Last edited by gridvvk; March 12th 2013 at 12:55 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Oct 2009

    Re: Question on composition of functions

    Concerning (b), you may find this post helpful. It's not exactly the same problem, so feel free to post your thoughts.
    Thanks from gridvvk
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: March 5th 2012, 05:34 PM
  2. Replies: 2
    Last Post: November 8th 2011, 09:13 PM
  3. Question about Composition Functions
    Posted in the Algebra Forum
    Replies: 12
    Last Post: September 13th 2011, 07:30 PM
  4. Another composition of functions question
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 17th 2010, 06:40 AM
  5. Replies: 1
    Last Post: November 5th 2009, 04:30 PM

Search Tags

/mathhelpforum @mathhelpforum