What value(s) must be excluded from the domain of `f(x)=(x+2)/(x-2)`?

Options

A. `-2`
B. 0
C. 2
D. 2 and -2

Explanation

To determine the value(s) that must be excluded from the domain of the function \( f(x) = \frac{x + 2}{x - 2} \), we need to analyze the function, particularly the denominator.

### Step-by-Step Solution:

1. **Identify the Function**:
We have the function \( f(x) = \frac{x + 2}{x - 2} \).

2. **Determine the Denominator**:
The denominator of the function is \( x - 2 \).

3. **Set the Denominator to Zero**:
To find the values that must be excluded from the domain, we set the denominator equal to zero:
\[ x - 2 = 0 \]

4. **Solve for \( x \)**:
Solving the equation \( x - 2 = 0 \) gives:
\[ x = 2 \]

5. **Conclusion**:
The value \( x = 2 \) must be excluded from the domain of the function \( f(x) \) because it would make the denominator zero, which is undefined in mathematics.

### Final Answer:
The value that must be excluded from the domain of \( f(x) \) is \( x = 2 \).

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