If `f: R to R ` be defined by `f(x) =(1)/(x), AA x in R.` Then , f is

Options

A. one-one
B. onto
C. bijective
D. f is not defined

Explanation

To determine the nature of the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = \frac{1}{x} \), we need to analyze its properties, particularly its domain and whether it is defined for all real numbers.

### Step-by-Step Solution:

1. **Identify the Function**:
We are given the function \( f(x) = \frac{1}{x} \).

2. **Determine the Domain**:
The function \( f(x) = \frac{1}{x} \) is defined for all real numbers except where the denominator is zero. Therefore, we need to find where \( x \) makes the denominator zero.

3. **Check for Undefined Points**:
Set the denominator equal to zero:
\[ x = 0 \]
At \( x = 0 \), \( f(0) = \frac{1}{0} \), which is undefined (or can be considered as approaching infinity).

4. **Conclusion about the Domain**:
Since the function is not defined at \( x = 0 \), the domain of \( f \) is all real numbers except zero. We can express this as:
\[ \text{Domain of } f = \mathbb{R} \setminus \{0\} \]

5. **Final Statement**:
Therefore, the function \( f(x) = \frac{1}{x} \) is not defined for \( x = 0 \), and thus, it is not a function from \( \mathbb{R} \) to \( \mathbb{R} \) in the strict sense, as it does not provide an output for every input in \( \mathbb{R} \).

### Answer:
The function \( f \) is not defined for \( x = 0 \).

---