https://file.aiquickdraw.com/mathbot/file/1727190521554f7dhi8yv.jpg

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.

Find the points where the function f(x) = 1 / (x^2 - 3x + 2) is undefined.

Solve for the points where the rational function f(x) = 1 / (x^2 - 3x + 2) is undefined by factoring the quadratic equation. Learn about rational functions and how to handle undefined points in algebra. Ideal for students in Grades 9-11.

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