Let f : R → R be the function with formula f(x) = x 3−x 2 = x 2 (x−1). (i) Graph this function (figure out where it is zero, positive and negative). (ii) (a) Find (nonempty) sets X, Y ⊂ R so that the restriction f|X is a bijection from X onto Y . (b) Is there a maximal choice for X? i. e. is there a set X with this property and also such that no set larger that X has this property? If there is, is it unique? (c) Is there a maximal choice for Y ? If there is, is that unique?