State the domain of these functions :
`F:xto(6)/(x)`

Answer

To find the domain of the function \( f(x) = \frac{6}{x} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the Function**: The given function is \( f(x) = \frac{6}{x} \).

2. **Determine Restrictions**: The function involves a fraction where \( x \) is in the denominator. A fraction is undefined when the denominator is zero. Therefore, we need to find when \( x = 0 \).

3. **Set the Denominator to Zero**:
\[ x = 0 \]
This indicates that at \( x = 0 \), the function \( f(x) \) is undefined.

4. **Conclusion on Domain**: Since the function is defined for all real numbers except for \( x = 0 \), we can express the domain in set notation. The domain of \( f(x) \) is:
\[ \text{Domain of } f(x) = \{ x \in \mathbb{R} \mid x \neq 0 \} \]
Alternatively, in interval notation, the domain can be expressed as:
\[ (-\infty, 0) \cup (0, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{6}{x} \) is all real numbers except 0, or in interval notation: \( (-\infty, 0) \cup (0, \infty) \).

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