Answer:
The domain = \(\{x\ |\ x\leq \frac{1}{2} ,\ x\in\mathbb{R}\}\)
Step-by-step explanation:
To find the domain of \(\sqrt{3-6x}\), 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 \((3-6x)\) has to be positive:
\(3-6x\geq 0\)
\(3\geq 6x\)
\(x\leq 3\div6\)
\(\displaystyle\bf x\leq \frac{1}{2}\)
Therefore, the domain = \(\{x\ |\ x\leq \frac{1}{2} ,\ x\in\mathbb{R}\}\)