Find the domain of the range of each of the following real functions:
`f(x)=(1)/(x-5)`

Explanation

To find the domain and range of the function \( f(x) = \frac{1}{x - 5} \), we will follow these steps:

### Step 1: Determine 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 because division by zero is undefined.

1. Set the denominator equal to zero:
\[ x - 5 = 0 \]
2. Solve for \( x \):
\[ x = 5 \]
3. Therefore, the function is undefined at \( x = 5 \). Thus, the domain of \( f(x) \) is all real numbers except 5.

**Domain**:
\[ \text{Domain} = \mathbb{R} \setminus \{5\} \]

### Step 2: Determine the Range
To find the range, we analyze the output values \( f(x) \) can take.

1. Rewrite the function in terms of \( y \):
\[ y = \frac{1}{x - 5} \]
2. Rearranging gives:
\[ y(x - 5) = 1 \quad \Rightarrow \quad yx - 5y = 1 \quad \Rightarrow \quad yx = 1 + 5y \]
3. Solving for \( x \):
\[ x = \frac{1 + 5y}{y} \]
4. The expression \( \frac{1 + 5y}{y} \) is defined for all \( y \) except when \( y = 0 \) (since division by zero is undefined).

Thus, \( y \) can take any real number value except for 0.

**Range**:
\[ \text{Range} = \mathbb{R} \setminus \{0\} \]

### Final Answer
- **Domain**: \( \mathbb{R} \setminus \{5\} \)
- **Range**: \( \mathbb{R} \setminus \{0\} \)