Which equation can be simplified to find the inverse of y = 2x2?
StartFraction 1 Over y EndFraction = 2 x squared
y = one-half x squared
–y = 2x2
x = 2y2

To find the inverse of the equation \( y = 2x^2 \), we follow these steps:

1. Start with the equation: \( y = 2x^2 \).
2. Solve for \( x \) in terms of \( y \) by isolating \( x \):
   \[
   \frac{y}{2} = x^2
   \]
   \[
   x = \pm \sqrt{\frac{y}{2}}
   \]

3. Now, swap \( x \) and \( y \) to get the inverse function:
   \[
   y = \pm \sqrt{\frac{x}{2}}
   \]

The correct simplified equation for finding the inverse is not explicitly listed, but it is closest to:

**None of the listed options directly represent the inverse.**

Would you like more details or have any questions about the steps? Here are five related questions to deepen understanding:

1. How do you derive the inverse of a function step-by-step?
2. Why do we swap \( x \) and \( y \) when finding an inverse function?
3. What does the inverse function represent in this context?
4. Can all quadratic functions have inverses?
5. How does restricting the domain of \( y = 2x^2 \) affect the inverse?

**Tip:** The square root introduces both positive and negative solutions, so restrict the domain if the function must be one-to-one.

Which equation can be simplified to find the inverse of y = 2x^2? StartFraction 1 Over y EndFraction = 2 x squared y = one-half x squared –y = 2x2 x = 2y2

Learn how to find the inverse of the quadratic function y = 2x^2 through step-by-step instructions. This guide explores key algebraic concepts, including isolating x, using square roots, and swapping variables. Suitable for students in Grades 10-12.

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