The given function in the image is:

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

The problem asks to find the points where $f(x)$ is undefined.

For a rational function, $f(x)$ is undefined when the denominator is equal to zero. So, we need to solve the equation:

$x^2 - 3x + 2 = 0$

This is a quadratic equation. Let's factor it:

$x^2 - 3x + 2 = (x - 1)(x - 2) = 0$

The solutions to this equation are:

$x = 1 \quad \text{or} \quad x = 2$

Thus, $f(x)$ is undefined at $x = 1$ and $x = 2$.

Would you like a detailed explanation of the factoring method used here?

Here are 5 related questions to expand this topic:

1. How can we determine if a function is undefined without solving for specific points?
2. What happens graphically at points where a function is undefined?
3. How can we solve more complex rational functions for undefined points?
4. How does the concept of discontinuity relate to functions being undefined?
5. Can a rational function be undefined at more than two points?

Tip: Always check the denominator of a rational function for zeros to find where it might be undefined.