Let x∗ be an attracting fixed point under a continuous map f. If the immediate basin of attraction B(x∗)=(a, b), show that the set {a, b} is invariant. Then conclude that there are only three...

Let x∗ be an attracting fixed point under a continuous map f. If the immediate basin of attraction B(x∗)=(a, b), show that the set {a, b} is invariant. Then conclude that there are only three scenarios in this case: (1) both a and b are fixed points, or (2) a or b is fixed and the other is an eventually fixed point, or (3) {a, b} is a 2-cycle.