If `f(x)=(x-5)/(5-x)` then find dom (f) and range (f).

Explanation

To find the domain and range of the function \( f(x) = \frac{x-5}{5-x} \), we will follow these steps:

### Step 1: Identify the Domain
The domain of a function consists of all the values of \( x \) for which the function is defined. In this case, we need to ensure that the denominator is not equal to zero.

1. Set the denominator equal to zero:
\[ 5 - x = 0 \]
Solving for \( x \):
\[ x = 5 \]
Therefore, \( x \) cannot be equal to 5.

2. Thus, the domain of \( f \) is all real numbers except \( x = 5 \):
\[ \text{Domain} = \mathbb{R} \setminus \{5\} \]

### Step 2: Simplify the Function
Next, we will simplify the function to understand its behavior better.

1. Rewrite the function:
\[ f(x) = \frac{x - 5}{5 - x} \]
Notice that \( 5 - x = -(x - 5) \), so we can rewrite the function:
\[ f(x) = \frac{x - 5}{-(x - 5)} = -1 \quad \text{for } x \neq 5 \]

### Step 3: Identify the Range
Since \( f(x) = -1 \) for all \( x \) in the domain, the range of the function is simply the value that \( f(x) \) takes.

1. Therefore, the range of \( f \) is:
\[ \text{Range} = \{-1\} \]

### Final Answer
- **Domain**: \( \mathbb{R} \setminus \{5\} \)
- **Range**: \( \{-1\} \)