Question

determinati domeniul de definitie al functiei :f:D->R,f(x)=radical din 24x-96 supra x-6

Answer 1

   
[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]