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

Options

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

Answer

To determine the domain of the function \( f(x) = x \), we need to analyze the function and identify the set of all possible input values (x-values) that can be used in the function.

### Step-by-Step Solution:

1. **Understanding the Function**:
The function \( f(x) = x \) is a linear function where the output is equal to the input. This means for every x-value, there is a corresponding y-value which is the same.

2. **Identifying Restrictions**:
We need to check if there are any restrictions on the values of x. For most polynomial functions, including linear functions like \( f(x) = x \), there are no restrictions.

3. **Considering the Real Number Line**:
The x-values can extend infinitely in both the positive and negative directions. This means:
- As \( x \) approaches positive infinity, \( f(x) \) also approaches positive infinity.
- As \( x \) approaches negative infinity, \( f(x) \) also approaches negative infinity.

4. **Conclusion on the Domain**:
Since there are no restrictions on the values of x, the domain of the function \( f(x) = x \) is all real numbers. In interval notation, this is expressed as:
\[ \text{Domain} = (-\infty, \infty) \]
Alternatively, we can also express this as:
\[ x \in \mathbb{R} \]

### Final Answer:
The domain of the function \( f(x) = x \) is \( (-\infty, \infty) \) or \( x \in \mathbb{R} \).

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