Math Problem Statement

Simplify or analyze the function f(x) = (4 - 3x - x^2) / (x^2 - 1)

Solution

The given function f(x)f(x) from the image is:

f(x)=4−3x−x2x2−1f(x) = \frac{4 - 3x - x^2}{x^2 - 1}

Would you like to solve this equation, analyze its properties (like asymptotes or domain), or find something specific, such as the derivative or integral?

Here are a few possible next steps:

  1. Simplify the function and identify any factorization.
  2. Find the domain of f(x)f(x).
  3. Identify any vertical or horizontal asymptotes.
  4. Take the derivative to analyze the function’s behavior.
  5. Find the critical points and analyze them for extrema.

Tip: If the denominator equals zero, the function is undefined at those points, which could help you find vertical asymptotes or restrictions in the domain.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Asymptotes
Domain and Range

Formulas

Quadratic formula: ax^2 + bx + c = 0
Difference of squares: a^2 - b^2 = (a - b)(a + b)

Theorems

Asymptote Theorem
Factorization of Quadratic Expressions

Suitable Grade Level

Grades 9-12

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