The given function appears to be:

$f(x) = 3 - \sqrt{6 - 2x}$

To find the domain of this function:

The domain of a function refers to all the values of $x$ for which the function is defined. Since the function involves a square root, the expression inside the square root must be non-negative because the square root of a negative number is not a real number.

Step 1: Set the expression inside the square root to be greater than or equal to zero.

$6 - 2x \geq 0$

Step 2: Solve the inequality.

$6 \geq 2x$ $x \leq 3$

Thus, the function is defined for $x \leq 3$.

Final Domain:

The domain of the function is: $(-\infty, 3]$

Let me know if you have questions or want more details! Here are a few related questions:

1. How do you solve square root inequalities like the one in this problem?
2. What happens to the domain if the function was $f(x) = \sqrt{6 - 2x} + 3$?
3. What is the range of the function $f(x) = 3 - \sqrt{6 - 2x}$?
4. How do you find the domain of a rational function?
5. What is the difference between domain and range in a function?

Tip: Always remember that square roots in real functions are only defined for non-negative numbers.