Find the points of discontinuity of the following function
f(x) = 4 if x is a rational number and x^2 if x is an irrational number
I know that the function will only be continuous at +/- 2. But I need to prove it. I am not sue how to go about it. I am sure we need to use the sequential criterion for continuity to show that lim f(xn) <> f(c) when lim xn = c. We can take a sequence of irrationals that converges to a rational number and a sequence of rationals that converges to an irrational. Is this right?