Question

If we have the function f(x) = (ax + b) / (cx + d) with a,b,c,d real numbers for which values of a,b,c,d is the following true

f(f(x)) for all x

I do a whole lot of algebra and get that that a,b,c,d must satisfy some conditions :

c*(a+d) = 0
(d^2) - (a^2) = 0
-b *(a+b) = 0

But I'm not sure, should I try solving the system or what, somehow I feel my approach is wrong

Answer 1

Sorry the condition that must be satisfied is f(f(x)) = x for all x