let f(x) be continuous for 0<=f(x)<=1. suppose that f(x) assumes rational vlaues only and that f(x)=1/2 when x=1/2. prove that f(x)=1/2 everywhere. im having trouble with this simple question, here's what i did: |x-1/2|<d implies |f(x)-1/2|<e. f(x) assumes only rational values so ( im guessing that by 'assumes' it's input is rational values, so |x-x0|<d |f(x)-f(x0)|<e f(x0)=p/q if p/q>1/2 then |f(x)-p/q|<|f(x)-1/2|<=e and if p/q<1/2 |f(x)-1/2|<|f(x)-p/q|<e, and thus the limit of f(x) at x0 always converges to 1/2. is this right?