Domain of the functions f defined b `f(x) = (5-x)/(x-5)` is

Options

A. R
B. R - {1}
C. R - {5}
D. R - {-4}

Answer

To find the domain of the function \( f(x) = \frac{5 - x}{x - 5} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the Function**:
The function is given as:
\[ f(x) = \frac{5 - x}{x - 5} \]

2. **Determine the Denominator**:
The denominator of the function is \( x - 5 \). For the function to be defined, the denominator must not be equal to zero.

3. **Set the Denominator Not Equal to Zero**:
We set up the inequality:
\[ x - 5 \neq 0 \]

4. **Solve the Inequality**:
Solving the inequality gives:
\[ x \neq 5 \]

5. **State the Domain**:
The domain of the function is all real numbers except \( x = 5 \). In interval notation, this can be expressed as:
\[ (-\infty, 5) \cup (5, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{5 - x}{x - 5} \) is:
\[ (-\infty, 5) \cup (5, \infty) \]