The domain of f(x) = `(x^(2))/(x^(2) - 3x + 2)` is :

Options

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

Answer

To find the domain of the function \( f(x) = \frac{x^2}{x^2 - 3x + 2} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero.

### Step-by-Step Solution:

1. **Identify the Denominator**:
The denominator of the function is \( x^2 - 3x + 2 \).

2. **Set the Denominator Equal to Zero**:
To find the values of \( x \) that make the function undefined, we set the denominator equal to zero:
\[ x^2 - 3x + 2 = 0 \]

3. **Factor the Quadratic Equation**:
We can factor the quadratic expression:
\[ x^2 - 3x + 2 = (x - 1)(x - 2) \]

4. **Find the Roots**:
Setting each factor to zero gives us the roots:
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]

5. **Determine the Domain**:
The function is undefined at \( x = 1 \) and \( x = 2 \). Therefore, the domain of \( f(x) \) includes all real numbers except these two values:
\[ \text{Domain of } f(x) = \mathbb{R} \setminus \{1, 2\} \]

### Final Answer:
The domain of \( f(x) = \frac{x^2}{x^2 - 3x + 2} \) is all real numbers except \( 1 \) and \( 2 \).

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