1. Define the "tent map," T: [0, 1] [0, 1]: T(x) = { J 2x, 2-2x, and define the "doubling map*," D: [0, 1] [0, 1]: 2x, 2x-1, 0, D(x) = if 0 < x < 1/1, xi. if if 0 < x < 1/1, if x < 1, if x = 1, *Beware: This definiton is slightly different than the definition givein in the textbook and in class. i) Determine the function DoT(x), i.e., the composition of the functions D(T(x)). Justify carefully. ii) Sketch by hand the graph of DoT(r) labelling it appropriately. (Indicate ponts of discontinuity with filled and unfilled dots. In particular, what is Do T() and indicate what this is clearly on the graph. iii) Find all fixed points of DoT(r) and determine if they are attracting or repelling, analytically.