8. (a) The point x = 0 is a fixed point, so doesn't converge to 1 - 1/s. The point x = 1 goes to x = 0. All x, 0 < x < 1, converge to 1 - 1/s.
(b) The point 1 - 1/s is fixed, and even though it is unstable, starting exactly there the iteration stays there. To find other points not converging to the stable 2-cycle, reverse graphical iteration from the fixed point. This produces two infinite sequences of points (one accumulating at x = 0, the other at x = 1) going to the fixed point, hence not converging to the 2-cycle. Of course, x = 0 and x = 1 behave as they did in (a), and so don't converge to the 2-cycle. The inverse graphical iteration process is illustrated by the dashed lines in the figure below (s = 3.4).

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