For each nonzero rational number x, write x as p /q where p, q are integers with no common factors and q > 0, and then define f(x) = 1 /q . Also define f(0) = 1 and f(x) = 0 for all x R\Q. Thus f(x)=1 for each integer, f( 1 /2 ) = f(1/ 2 ) = f( 3 /2 ) = = 1/ 2 , etc. Show f is continuous at each point of R \ Q and discontinuous at each point of Q.