A function is said to be bijective if it is both one-one and onto, Consider the mapping `f : A rarr B` be defined by `f(x) = (x-1)/(x-2)` such that f is a bijection.
Domain of f is

Options

A. reflexive
B. `R - {2}`
C. `R - {0}`
D. `R - {1, 2}`

Answer

To find the domain of the function \( f(x) = \frac{x-1}{x-2} \), we need to ensure that the function is defined for all values of \( x \). Since this is a rational function, it is defined as long as the denominator is not equal to zero.

### Step-by-Step Solution:

1. **Identify the function**: We have the function defined as:
\[ f(x) = \frac{x-1}{x-2} \]

2. **Set the denominator not equal to zero**: The function will be undefined when the denominator is zero. Therefore, we need to solve the equation:
\[ x - 2 \neq 0 \]

3. **Solve for \( x \)**: From the equation \( x - 2 \neq 0 \), we can find:
\[ x \neq 2 \]

4. **Determine the domain**: The domain of the function is all real numbers except \( x = 2 \). In interval notation, this can be expressed as:
\[ \text{Domain of } f = (-\infty, 2) \cup (2, \infty) \]

### Final Answer:
The domain of the function \( f(x) = \frac{x-1}{x-2} \) is:
\[ (-\infty, 2) \cup (2, \infty) \]