Function problems Find all functions of the form
$$f(x)=\frac{b}{cx+1}$$
where $b$ and $c$ are integers, and for all real numbers x such that $f(f(f(x)))$ is defined the following equation holds:
$$f(f(f(x)))=x$$
I'm not really sure how to go about this question, only that $f(x)=1/x$, and that $f(f(x))$=$\frac{b}{c\frac{b}{cx+1}+1}$ will most likely be used. Any solutions or tips to point me in the right direction will be greatly appreciated. Thanks

HINT: after substitution three times for $x$ the given term we get the equation
$$\frac{b (b c+c x+1)}{b c^2 x+2 b c+c x+1}=x$$
can you finish?
