Math Problem Statement

Solve and tell the correct option

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

Solution

We are given the function f(x)=x2x1f(x) = \frac{x - 2}{x - 1}, and we need to find f(1)f(-1).

Step 1: Substitute x=1x = -1 into the function

f(1)=1211=32f(-1) = \frac{-1 - 2}{-1 - 1} = \frac{-3}{-2}

Step 2: Simplify the expression

f(1)=32f(-1) = \frac{3}{2}

Conclusion:

The value of f(1)f(-1) is 32\frac{3}{2}.

The correct answer is the third option: 32\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)f(0) for the same function?
  2. How would you find the domain of f(x)f(x)?
  3. What is the value of f(1)f(1), and why is it undefined?
  4. Can you express f(x)=x2x1f(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!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Rational Expressions

Formulas

Substituting values into functions
Simplifying fractions

Theorems

None explicitly required; focuses on basic algebraic manipulation

Suitable Grade Level

Grades 9-10