Chapter 2 - Section 2.2 - Limit of a Function and Limit Laws - Exercises - Page 66: 9

$f(x)$ does not need to be defined at $x=1$ and nothing else can be said.

The existence and non-existence of the limit as x approaches c does not depend on whether the function is defined or not defined at x=c. So f(x) does not need to be defined at $x=1$ and nothing can be said.