What Values of a, b, c, and d Make f(f(x)) = x for All x?

[pyrosilver]

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

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.

 

[n!kofeyn]

Now set that equal to x (i.e., set f(f(x))=x). Then start solving for a,b,c,d.