Question

If f(x)={12, if x in an integer} find wether f is continuous at x=9

Answer 1

f(x) = {12, if x is an integer}

$f(9)=12$

$\lim_{x \to 9-} f(9)=$ not defined

$\lim_{x \to 9+} f(9)=$ not defined

Since $\lim_{x \to 9-} f(9) \neq f(9) \neq \lim_{x \to 9+} f(9)$, it is not continuous at x=9.