f(2) not defined in this piecewise function Find all points of discontinuity:
$$f(x) =
\begin{cases}
x+2,  & \text{if $x > 2$} \\[2ex]
x^2, & \text{if $x < 2$}
\end{cases}$$
I currently am not sure at all if my workings of this problem is correct but this is what i got:
the lim exists and it is 4 BUT what i dont know is if $f(2)$ exists as it is not defined if $x = 2$ etc
SO... my conclusion is: f(x) is discontinuous at x = 2
please correct me if i am wrong, because i am uncertain about my interpretation, thanks!.

Domain of $f$ is a disconnected set,$(-\infty,2)\cup(2,\infty)$ in $\Re$. Also f is continuous in each of these intervals as mentioned in the 'comments'. We can not talk of f being continous or discontinous at 2 as $2\notin D_f$.
