Math Help - Use algebra to identify the points of the 2-cycle?

1. Use algebra to identify the points of the 2-cycle?

f(x) = 9/x + x/2 - c

c ≤ 3.5

I'm pretty sure you just have to solve f(f(x))-x = 0. But, that doesn't seem possible...

2. Originally Posted by Mitchell
f(x) = 9/x + x/2 - c

c ≤ 3.5

I'm pretty sure you just have to solve f(f(x))-x = 0. But, that doesn't seem possible...
Why not? f(f(x))= f(9/x+ x/2- c)= 9/(9/x+ x/2+ c)+ (9/x+ x/2+ c)/2- c= 9x/(9- x^2+ cx)+ 9/(2x)+ x/4+ c/2.

So you want to solve
$\frac{9x}{9- x^2+ cx}+ \frac{9}{2x}+ x/4+ c/2- x= 0$
Difficult perhaps but possible.