Question

Calc piece wise help please. Suppose f(x) =
{x if x is rational
{0 if x is irrational

Find all the points where f is continuous, anyone know how to solve this?

Answer 1

can you elaborate on that?

Answer 2

Suppose say x=3, so x is rational so f(x)=3,
Let \(y_n=3+\frac {\sqrt 2}n \)then\( y_n\) is irrational.
Notice that \(y_n \)converges to 3 but\( f(y_n)=0\) so it does not converge to 3, hence f is not continuous at x=3. The same reasoning applies for x being any rational number different from zero.
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Answer 3

Try to see why it is not continuous at any a irrational such that a is different from zero.