Hi everyone,

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.

Solution:

When

Hence f is discontinuous at x=1

When

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.