I need your idea about the way in which I had done the following question. Although this could be proved using the "sequential criterion of continuity" I want to know whether my way of doing it is correct or not.
Note:Q denotes rational numbers and P denotes irrational numbers.
Show that f is discontinuous at x=1 and continuous at x=2. Is it true that f is continuous only at x=2? Justify your answer.
Hence f is discontinuous at x=1
Hence by the 3-point definition of continuity f(x) is continuous at x=2.
Is it true that f is continuous only at x=2?
No. Consider x=0; It could be shown using the previous method that x is continuous at x=0.
Your generosity is greatly appreciated.