The domain of the function `f(x)=(1)/(x)` is :

Options

A. R
B. `R^(+)`
C. `R-{0}`
D. `R^(+)uu{0}`

Answer

To find the domain of the function \( f(x) = \frac{1}{x} \), 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 \( f(x) = \frac{1}{x} \).

2. **Determine where the function is undefined**: The function \( f(x) \) is undefined when the denominator is zero. Therefore, we need to find when \( x = 0 \).

3. **Set up the condition**: We set the denominator equal to zero to find the problematic value:
\[ x = 0 \]

4. **Exclude the problematic value**: Since the function is undefined at \( x = 0 \), we must exclude this value from the domain.

5. **Express the domain**: The domain of the function can be expressed in interval notation as:
\[ (-\infty, 0) \cup (0, +\infty) \]
This means that \( x \) can take any real number except for zero.

### Final Answer:
The domain of the function \( f(x) = \frac{1}{x} \) is \( (-\infty, 0) \cup (0, +\infty) \).

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