Math Problem Statement

What is the function given in the image?

Solution

The function given in the image is:

f(x)=3x+7x22f(x) = \frac{3x + 7}{x^2 - 2}

Would you like me to evaluate this function for specific values of xx, find its derivative, integral, or something else? Let me know!

Five follow-up questions:

  1. Do you want to find the domain of the function?
  2. Would you like to find the vertical or horizontal asymptotes?
  3. Should I compute the derivative of the function?
  4. Do you want to analyze the function for local maxima or minima?
  5. Are you interested in finding where the function is increasing or decreasing?

Tip:

For rational functions like this one, always check for points where the denominator is zero to determine the domain and possible vertical asymptotes!

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Math Problem Analysis

Mathematical Concepts

Rational Functions
Asymptotes
Derivatives
Function Analysis

Formulas

f(x) = (3x + 7) / (x^2 - 2)
Derivative formula for a quotient
Horizontal and Vertical Asymptotes

Theorems

Quotient Rule for Derivatives
Rules for Finding Asymptotes

Suitable Grade Level

Grades 10-12