If the function f : `A rarr ` B is defined as f(x) `= (x-2)/(x-3) ` then the set A must be

Options

A. R
B. R - {3}
C. R - {1}
D. R - { 2}

Answer

To determine the set \( A \) for the function \( f(x) = \frac{x-2}{x-3} \), we need to find the domain of the function. The domain consists of all the values of \( x \) for which the function is defined.

### Step-by-Step Solution:

1. **Identify the function**:
The function is given as \( f(x) = \frac{x-2}{x-3} \).

2. **Determine where the function is undefined**:
A rational function is undefined when the denominator is equal to zero. Therefore, we need to find the value of \( x \) that makes the denominator zero:
\[ x - 3 = 0 \]
Solving this gives:
\[ x = 3 \]

3. **Define the domain**:
Since the function is undefined at \( x = 3 \), we must exclude this value from the set of all real numbers. The domain of the function can be expressed as:
\[ A = \mathbb{R} - \{3\} \]
This means that the set \( A \) includes all real numbers except for 3.

4. **Final answer**:
Therefore, the set \( A \) is:
\[ A = \mathbb{R} - \{3\} \]