Math Problem Statement

Df

Determine the mathematical details and analysis for the function \(f(x) = \frac{\sqrt{x^2 - 1} + 3x}{x}\).

Solution

The function provided in the image is:

f(x)=x2−1+3xx.f(x) = \frac{\sqrt{x^2 - 1} + 3x}{x}.

Would you like me to simplify, analyze, or solve any specific aspect of this function (e.g., domain, derivative, asymptotes)? Let me know!

Related Questions:

  1. What is the domain of f(x)f(x)?
  2. How do you calculate the derivative of f(x)f(x)?
  3. Can f(x)f(x) be simplified further?
  4. What are the horizontal and vertical asymptotes of f(x)f(x)?
  5. What is the behavior of f(x)f(x) as x→∞x \to \infty?

Tip:

Always check the domain restrictions caused by square roots and denominators in any function to avoid undefined expressions!

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Math Problem Analysis

Mathematical Concepts

Functions
Rational Expressions
Square Roots
Domain Analysis

Formulas

Domain restrictions: square root \(\sqrt{u}\) requires \(u \geq 0\)
Rational expression \(\frac{p(x)}{q(x)}\): denominator \(q(x) \neq 0\)

Theorems

Domain of a function
Simplification and rationalization of expressions

Suitable Grade Level

Grades 10-12

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