Math Problem Statement

f(x) = (3x^2 - 48) / (x^2 - 4x)

Solution

The given function is:

f(x)=3x2−48x2−4xf(x) = \frac{3x^2 - 48}{x^2 - 4x}

Would you like me to:

  • Simplify the function?
  • Find the domain and range?
  • Solve for xx where f(x)=0f(x) = 0?
  • Analyze its asymptotes and other properties?

Let me know how you'd like to proceed! Here are some potential next questions:

  1. Would you like to simplify the expression further?
  2. Should I find the vertical and horizontal asymptotes?
  3. Do you want to factor both the numerator and the denominator?
  4. Should we investigate the domain restrictions of the function?
  5. Are you interested in graphing the function?

Tip: To analyze rational functions, always consider factoring both the numerator and the denominator to identify common terms and possible simplifications.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Factoring
Simplification

Formulas

Rational function: f(x) = (P(x))/(Q(x))
Factoring quadratic expressions

Theorems

Rational Function Theorem
Zero-Product Property

Suitable Grade Level

Grades 10-12

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