[tex]\displaystyle\\
\bf\\
f:D \rightarrow R,~~ f(x)= \frac{ \sqrt{24x-96} }{x-6} \\\\
\text{Punem urmatoarele conditii:}\\\\
1) ~\text{Expresia de sub radical trebuie sa fie pozitiva.}\\
2)~\text{Expresia de la numitor trebuie sa fie diferita de zero.}\\\\
24x-96 \geq 0\\
24x \geq 96\\\\
x \geq \frac{96}{24} \\\\
x \geq 4 \\\\x \in [4;~\infty)\\\\
x-6 \neq 0\\
x \neq 6\\\\
\Longrightarrow ~~~\boxed{D = [4;~\infty) / \{6\}}~~~sau~~~\boxed{D = [4;~6)\bigcup (6;~+\infty)}[/tex]
