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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.

Find the domain of f(x) = 3 - √(6 - 2x).

Learn how to find the domain of the function f(x) = 3 - √(6 - 2x). This problem covers important algebraic concepts, such as solving inequalities for square roots, and is suitable for students in Grades 9-11.

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