1. The problem statement, all variables and given/known data I am told to prove or disprove whether the following function is 1:1 and onto. f(x)= x if x is rational x^2 if x is not rational The Domain and Range are both given as [0,1] I have provided a counter example to show it is not 1:1. x=1/2 and sqrt(0.5) both map to 0.5. I am stuck on onto. If I am to disprove it being onto, I need to find/show there is a b in the range such that there is no a in the range for which (a,b) is an element of f(a). I am confused as to where to begin to formulate this.