This is Dynamical Systems, specifically a discrete system. We are using L and R as in Left and Right such as:
L=[0,0.5]
R=(0.5,1]
and LL=[0,0.25]
LR=(0.25,0.5] and so on like that. We keep splitting the interval in halves, where L represents left and R represents right.
Also this is a Logistic Map between [0,1] only.
Q:You have f(x)=4x(1−x) and xo element of LLRRRRLRRLR;
b) Is f^{8}(x_o) greater than (>), equal to (=) or less than (<) 1/2?
Here f^{8}(x_o) means f(f(f(f(f(f(f(f(x_o)))))))).
They want to know if that is greater than, equal to or less than one half.
A: I got a & c, which I omitted.
I'm stuck for b), I have no way to know how to compute the 8th iteration of the function f at x_o. Does it have something to do with LLRRRRLRRLR?
Thanks,