\[f(x) = \sqrt{x - 4} + \frac{x - 12}{x^{2} - 16},\ \ \]
\[\left\{ \begin{matrix}
x - 4 \geq 0 \\
x^{2}
eq 16\ \ \ \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix}
x \geq 4\ \ \ \\
x
eq \pm 4 \\
\end{matrix} \right.\ \text{\ \ }\]
\[D(f) = (4; + \infty).\]