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 a rational function, which means it is defined for all real numbers except where the denominator is equal to zero.

### Step 1: Set the denominator equal to zero
We start by finding the values of \( x \) that make the denominator zero:
\[ x^2 - 3x + 2 = 0 \]

### Step 2: Factor the quadratic equation
Next, we factor the quadratic equation:
\[ x^2 - 3x + 2 = (x - 1)(x - 2) = 0 \]

### Step 3: Solve for \( x \)
Setting each factor equal to zero gives us:
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]

### Step 4: Identify the values to exclude from the domain
The values \( x = 1 \) and \( x = 2 \) are where the function is undefined. Therefore, these values must be excluded from the domain.

### Step 5: Write the domain in interval notation
The domain of \( f(x) \) can be expressed in interval notation as:
\[ \text{Domain of } f(x) = \mathbb{R} - \{1, 2\} = (-\infty, 1) \cup (1, 2) \cup (2, \infty) \]

Thus, the domain of the function \( f(x) = \frac{x^2}{x^2 - 3x + 2} \) is:
\[ (-\infty, 1) \cup (1, 2) \cup (2, \infty) \]