$$ f: x \mapsto \sqrt{11-2 x} $$ Write an inequality for the numbers that must be excluded from the domain of $$ f $$.

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To determine which numbers must be excluded from the domain of the function $$ f(x) = \sqrt{11 - 2x} $$, we need to ensure that the expression inside the square root is non-negative.

### Step-by-Step Reasoning:

1. **Expression Inside the Square Root:**
   $$
   11 - 2x \geq 0
   $$
   
2. **Solving the Inequality:**
   $$
   11 \geq 2x \quad \Rightarrow \quad x \leq \frac{11}{2}
   $$
   
   This means that for the function to be defined, $$ x $$ must be less than or equal to $$ \frac{11}{2} $$.

3. **Excluding Values from the Domain:**
   The values that **must be excluded** from the domain are those that make the expression inside the square root negative:
   $$
   11 - 2x < 0 \quad \Rightarrow \quad x > \frac{11}{2}
   $$

### Final Answer:

All real numbers x greater than eleven-halves are excluded, that is, all x with x > 11⁄2.
All real numbers greater than 11⁄2 must be excluded from the domain of $$ f $$.

Write an inequality for the numbers that must be
excluded from the domain of .

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