Answer:
The domain = [tex]\{x\ |\ x\leq \frac{1}{2} ,\ x\in\mathbb{R}\}[/tex]
Step-by-step explanation:
To find the domain of [tex]\sqrt{3-6x}[/tex], we have to understand that in order that the range is in real number, then the function inside the square root has to be positive.
This means [tex](3-6x)[/tex] has to be positive:
[tex]3-6x\geq 0[/tex]
[tex]3\geq 6x[/tex]
[tex]x\leq 3\div6[/tex]
[tex]\displaystyle\bf x\leq \frac{1}{2}[/tex]
Therefore, the domain = [tex]\{x\ |\ x\leq \frac{1}{2} ,\ x\in\mathbb{R}\}[/tex]