What is the domain of the function `f(x)=(1)/(x-2)`?

Answer

To determine the domain of the function \( f(x) = \frac{1}{x - 2} \), we need to find the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the Function**:
The given function is \( f(x) = \frac{1}{x - 2} \).

2. **Understand When the Function is Undefined**:
A function is undefined when the denominator is equal to zero. Therefore, we need to find when \( x - 2 = 0 \).

3. **Solve for \( x \)**:
Set the denominator equal to zero:
\[ x - 2 = 0 \]
Solving this gives:
\[ x = 2 \]

4. **Determine the Domain**:
The function \( f(x) \) is undefined at \( x = 2 \). Thus, the domain of \( f(x) \) includes all real numbers except \( 2 \). In interval notation, this can be expressed as:
\[ (-\infty, 2) \cup (2, \infty) \]

5. **Final Answer**:
Therefore, the domain of the function \( f(x) = \frac{1}{x - 2} \) is:
\[ \text{Domain: } \mathbb{R} \setminus \{2\} \text{ or } (-\infty, 2) \cup (2, \infty) \]