Consider the map : [0, 1] [0, 1] given by x+1/2 f(x) = {...

 

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Consider the map ƒ : [0, 1] → [0, 1] given by x+1/2 f(x) = { 2 - 2x 0≤x≤ 1/2 1/2 ≤ x ≤ 1 (a) Show that it is continuous. (b) Show that it has a cycle of length 3. (c) Find all its cycles of lengths 1, 2, 3, and 4. Consider the map ƒ : [0, 1] → [0, 1] given by x+1/2 f(x) = { 2 - 2x 0≤x≤ 1/2 1/2 ≤ x ≤ 1 (a) Show that it is continuous. (b) Show that it has a cycle of length 3. (c) Find all its cycles of lengths 1, 2, 3, and 4.

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