Need help with a function problem?

  • Thread starter pyrosilver
  • Start date
  • #1
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Homework Statement



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)?

Homework Equations





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:

Answers and Replies

  • #2
537
3
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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