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.