\[f(x) = \sqrt{7 - x} - \sqrt{x - 7},\ \ \]
\[\left\{ \begin{matrix} 7 - x \geq 0 \\ x - 7 \geq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x \leq 7 \\ x \geq 7 \\ \end{matrix} \right.\ \]
\[\Longrightarrow D(f) = \left\{ 7 \right\}.\]