Math Problem Statement

y = (sqrt(x) - 1) / (sqrt(x) + 1)

Solution

The equation provided in the image is:

y=x1x+1y = \frac{\sqrt{x} - 1}{\sqrt{x} + 1}

Would you like to analyze this function further in terms of its properties such as:

  • Domain
  • Range
  • Asymptotes
  • Limits
  • Derivative or Integral

Let me know how you'd like to proceed or if you have any other questions.

Here are 5 related questions that can help deepen understanding:

  1. What is the domain of the function y=x1x+1y = \frac{\sqrt{x} - 1}{\sqrt{x} + 1}?
  2. What happens to the function as x0x \to 0?
  3. How does the function behave as xx \to \infty?
  4. What is the derivative of the function with respect to xx?
  5. Are there any horizontal or vertical asymptotes for this function?

Tip: When dealing with square root functions, always check if the domain is restricted by non-negative values, since x\sqrt{x} is defined only for x0x \geq 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Root
Rational Functions

Formulas

y = (sqrt(x) - 1) / (sqrt(x) + 1)

Theorems

Domain restrictions for square roots
Limits
Asymptotic behavior

Suitable Grade Level

Grades 10-12