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Homework Help: Need help with a function problem?

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data

    For which numbers a, b, c, and d will the function

    f(x) = (ax + b) / (cx + d)

    satisfy f(f(x)) = x for all x (for which this equation makes sense)?

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure what to do, which is my problem. So far I think that I can plug in (ax + b) / (cx + d) for x, because that is when it will satisfy f(f(x)) = x, right?

    So then I have:

    http://img26.imageshack.us/img26/6364/mathnumber8.jpg [Broken]

    So I'm not sure where I want to end up, or where to go from here :( Can someone help me? This is due tomorrow. All help is appreciated.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Oct 12, 2009 #2
    Now set that equal to x (i.e., set f(f(x))=x). Then start solving for a,b,c,d.
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