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(6pts. 3 points each) This question will examine Challenge 3. Please read pages 135 and 136 in the text. Let A1 be the rightmost subinterval whose left endpoint maps to the right of itself. Then f (A1) contains A1. (a): Step 1. Recall that the image of an interval under a continuous map is an interval. Use the fact that A g B => f(A) g f(B) to show that A1 Q f(A1) E f2lA1) E Hint: Use induction. (b): Step 2. Show that the number of orbit points :33- lying in fj (A1) is strictly increasing with j until all p points are contained in fk(A1) for a certain k. Explain why fk(A1) contains [$1,319]. Use the important facts that the endpoints of each subinterval are obliged to map to the subinterval endpoints from the partition. and that each endpoint must traverse the entire period-p orbit under f. X1 1 X9 ....LOO.O 4/'/ 4/4/ Figure 3.|4 Denition of 11.. A1 is chosen to be the rightmost subinterval whose leftrhand endpoint maps to the right under 3&quot