Find the domain of the following functions:
`(1)/(x-3)`

Answer

To find the domain of the function \( f(x) = \frac{1}{x - 3} \), we need to determine the values of \( x \) for which this function is defined.

### Step-by-Step Solution:

1. **Identify the Function**: We have the function \( f(x) = \frac{1}{x - 3} \).

2. **Determine the Denominator**: The function is in the form of \( \frac{a}{b} \), where \( a = 1 \) and \( b = x - 3 \). For this function to be defined, the denominator \( b \) must not be equal to zero.

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

4. **Solve for \( x \)**: To find the values that make the denominator zero, we solve the equation:
\[ x - 3 = 0 \implies x = 3 \]

5. **State the Domain**: Since the function is undefined at \( x = 3 \), the domain of \( f(x) \) includes all real numbers except 3. In interval notation, this can be expressed as:
\[ \text{Domain of } f(x) = (-\infty, 3) \cup (3, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{1}{x - 3} \) is all real numbers except 3, or in interval notation: \( (-\infty, 3) \cup (3, \infty) \).