Math Problem Statement

The user submitted an image showing three mathematical functions: f(x) = (x - 1) / (x + 2), f(x) = (2x - 5) / (x - 2), and f(x) = (x + 1) / (4 - x).

Solution

Thank you for sharing the image. From the image, we have three functions:

  1. f(x)=x−1x+2f(x) = \frac{x - 1}{x + 2}
  2. f(x)=2x−5x−2f(x) = \frac{2x - 5}{x - 2}
  3. f(x)=x+14−xf(x) = \frac{x + 1}{4 - x}

Let me know how you'd like me to proceed. Would you like:

  1. The domain of these functions?
  2. Simplifications or transformations of the expressions?
  3. Analysis of asymptotes and critical points?
  4. Something else?

Please specify! 😊

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Function Domains
Asymptotes

Formulas

Domain restriction: Denominator ≠ 0
Vertical asymptotes occur at values where the denominator is zero, provided the numerator does not also become zero

Theorems

Rules of rational functions for domain and asymptote analysis

Suitable Grade Level

Grades 9-12

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