Which equation can be simplified to find the inverse of y = 2x^2?

To find the inverse of the equation y = 2x², we need to express x in terms of y. First, we start by switching the variables, replacing y with x and x with y. This gives us:

x = 2y²

Next, we solve for y. To do that, we first isolate the term with y:

y² = ½x

Now, take the square root of both sides to solve for y:

y = ±√(½x)

However, since the original function y = 2x² is a parabola that opens upwards, we typically only consider the positive root when determining the inverse. Therefore, the inverse function can be expressed as:

y = √(½x)

In conclusion, the equation can be simplified to find its inverse by swapping the variables and then solving for y, leading us to our final expression.