Why is the following function discontinuous at the given number?

Question

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

Answer 1

The answer is c. f(2) is infinite (-∞) it approaches -∞ from either side of 2.

Jim