generate the square root function of y=x^2-2

The square root function of \( y = x^2 - 2 \) can be expressed as:

\[
y = \sqrt{x^2 - 2}
\]

This equation describes the positive square root of \( x^2 - 2 \). The domain of this function will only include values of \( x \) for which \( x^2 - 2 \geq 0 \), meaning \( x \leq -\sqrt{2} \) or \( x \geq \sqrt{2} \), because the expression inside the square root must be non-negative.

Would you like more details or have any specific questions?

Here are some related questions you might consider:
1. What is the domain and range of the function \( y = \sqrt{x^2 - 2} \)?
2. How would you graph \( y = \sqrt{x^2 - 2} \)?
3. Can this function have any negative outputs?
4. How do the solutions of \( y = \sqrt{x^2 - 2} \) compare to \( y = x^2 - 2 \)?
5. What is the derivative of \( y = \sqrt{x^2 - 2} \)?

**Tip**: Always check the domain of functions involving square roots, ensuring that the expression inside the root is non-negative for real-valued solutions.

generate the square root function of y = x^2 - 2

Explore the square root function y = \sqrt{x^2 - 2} and understand how to determine its domain and range. This solution dives into the algebraic manipulation of quadratic functions and square roots, making it ideal for high school students. Learn how to solve this type of function step-by-step, with tips for graphing and analysis.

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