1. The problem statement, all variables and given/known data Suppose f: [0,1] -> [0,1] is such that f attains each of its values exactly twice Show that f cannot be continuous 3. The attempt at a solution I assumed that f is continuous and tried to break it up into cases and show that there must be a value that is obtained 3 times. since f is defined on an interval it has a sup and an inf (each attained twice by hypothesis). my cases are the order in which the are attained, i.e. 1) max,min,max,min or 2) max,max,min,min case 1 is easy, but i can't figure out how to do case 2 is this the right approach or is there an easier way?