g(x)=0 if x is rational
g(x)=x if x is irrational
for what values of x is g continuous?
Have you ever heard of "Dirichelt" function?
Same idea.
The limit that we approach a point bt rationals needs to be the same as we approach the limit by irrationals. In that case $\displaystyle x=0$ is the only continous point.
Look Heir