Why is the following function discontinuous at the given number? $$f(x)= \ln{|x-2|},\ \ x=2$$
(a) $f(2)$ does not exist.
(b) $\displaystyle \lim_{x \to 2} f(x)$ does not exist (or is infinite).
(c) Both (a) and (b).
(d) $f(2)$ and $\displaystyle \lim_{x \to 2} f(x)$ exist, but they are not equal.