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.