Math Problem Statement

f(x) = x / (1 - 4x)

Solution

The function provided in the image is:

f(x)=x14xf(x) = \frac{x}{1 - 4x}

Let me know if you'd like me to solve or analyze this function further. For example, I can help with finding the domain, asymptotes, derivative, or other properties.

Here are a few questions related to this function:

  1. What is the domain of f(x)f(x)?
  2. How do you find the vertical asymptote of this function?
  3. What is the first derivative of f(x)f(x) and how can it be used to find critical points?
  4. How can you find the horizontal asymptote of this rational function?
  5. What are the intercepts of the function f(x)f(x)?

Tip: The domain of a rational function is all real numbers except where the denominator equals zero.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions

Formulas

f(x) = x / (1 - 4x)

Theorems

Rational Function Asymptote Theorem
Derivative

Suitable Grade Level

Grades 10-12