Answer
False.
Work Step by Step
If the limit has a value at a point, that does not necessarily mean the function is equal to the limit at that point.
For example $\lim\limits_{x\to 3}\dfrac{(x-3)(x-2)}{(x-3)}=1$ but $f(3)$ is undefined hence $f(3)\ne\lim\limits_{x\to3}f(x)$.
