پیوستگی تابع $f(x) = \left\{ \begin{gathered}
x - 5\,\,\,\,\,\,\,\,\,\,\,\,\,x \lt 2 \hfill \\
- 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 2 \hfill \\
{x^2} - 7\,\,\,\,\,\,\,\,\,\,x \gt 2 \hfill \\
\end{gathered} \right.$ را در $x = 2$ بررسی کنید.