Determine the domain for the following square root function.
\[
f(x)=-\sqrt{-6 x+3}
\]
$x \leq$
$x \geq$
Round your answer to three decimal places if necessary.
Answer
\(\boxed{x \leq \frac{1}{2}}\)
Step 1 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. For a square root function, the expression inside the square root must be greater than or equal to zero (since the square root of a negative number is not a real number). So, we need to solve the inequality -6x + 3 >= 0.
Step 2 ：Solving the inequality -6x + 3 >= 0, we get x <= 1/2.
Step 3 ：This means that the domain of the function f(x)=-sqrt{-6x+3} is all real numbers x such that x <= 1/2.
Step 4 ：\(\boxed{x \leq \frac{1}{2}}\)
