Let f: R->R be defined by
f(x)={x^{2} for x in Q, x+2 for x not in Q}
Find all points (if any) where f is continuous.
We learned that a function is continuous at a point where f(x)=limit as x->p f(x). I'm just not really sure how to go about finding these.
I think for all x in Q this function is discontinuous for all x not equal to zero, since that will be only case where f(x) will equal its limit. Is this correct thinking?