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The image you uploaded appears to contain a mathematical expression. Let me process and extract the information from it to provide a detailed explanation or solution. I will begin analyzing it now.The image contains a mathematical expression:

\[
f(x) = \frac{1}{x^2 - 3x + 2}
\]

This is a rational function. To analyze it, we should first identify its domain by determining where the denominator is zero (since division by zero is undefined).

### Finding the domain:

The denominator is \( x^2 - 3x + 2 \). We need to solve:

\[
x^2 - 3x + 2 = 0
\]

We can factor this quadratic expression:

\[
x^2 - 3x + 2 = (x - 1)(x - 2)
\]

Setting this equal to zero:

\[
(x - 1)(x - 2) = 0
\]

The solutions are:

\[
x = 1 \quad \text{or} \quad x = 2
\]

So, the function is undefined at \( x = 1 \) and \( x = 2 \).

### Domain:

The domain of \( f(x) \) is all real numbers except \( x = 1 \) and \( x = 2 \), or in interval notation:

\[
\text{Domain} = (-\infty, 1) \cup (1, 2) \cup (2, \infty)
\]

### Conclusion:

- The function \( f(x) \) is undefined at \( x = 1 \) and \( x = 2 \), where the denominator becomes zero.

Would you like further details or have any questions?

Here are 5 follow-up questions:
1. How do we find the vertical asymptotes of this rational function?
2. Can we determine the behavior of the function near \( x = 1 \) and \( x = 2 \)?
3. How would we find the horizontal or oblique asymptotes for this function?
4. What happens to the function as \( x \to \infty \) or \( x \to -\infty \)?
5. Could we sketch the graph of \( f(x) \) based on its domain and asymptotes?

**Tip**: Always check where a rational function's denominator is zero to find points where the function is undefined or where vertical asymptotes may occur.

Find the domain of the rational function f(x) = 1 / (x^2 - 3x + 2).

Learn how to find the domain of the rational function f(x) = 1 / (x^2 - 3x + 2). This problem involves factoring a quadratic expression and analyzing undefined points where the denominator equals zero. Suitable for high school students (Grades 10-12).

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