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We are given the function \( f(x) = \frac{x - 2}{x - 1} \), and we need to find \( f(-1) \).

### Step 1: Substitute \( x = -1 \) into the function
\[
f(-1) = \frac{-1 - 2}{-1 - 1} = \frac{-3}{-2}
\]

### Step 2: Simplify the expression
\[
f(-1) = \frac{3}{2}
\]

### Conclusion:
The value of \( f(-1) \) is \( \frac{3}{2} \).

The correct answer is the third option: \( \frac{3}{2} \).

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is \( f(0) \) for the same function?
2. How would you find the domain of \( f(x) \)?
3. What is the value of \( f(1) \), and why is it undefined?
4. Can you express \( f(x) = \frac{x-2}{x-1} \) in terms of partial fractions?
5. What are the horizontal and vertical asymptotes of the function?

**Tip**: Always check for points where the function might be undefined by considering values that make the denominator zero!

Find f(-1) when f is the function given by the rule f(x) = (x - 2) / (x - 1).

Solve the algebraic function f(x) = (x - 2) / (x - 1) by finding f(-1). Learn to substitute values into functions and simplify fractions. Suitable for students in Grades 9-10.

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