## Which Equation Can Be Simplified To Find The Inverse Of Y = 2X^{2}?

In mathematics, an inverse function is a function that “undoes” the effects of another function. To find the inverse of a function, one must “undo” the function in a way that gives the original input when given the output. When it comes to linear equations, the inverse is found by switching the x and y values and solving for y. However, for nonlinear equations, finding the inverse can be tricky.

### Finding the Inverse of a Nonlinear Equation: Y = 2X^{2}

In the equation **Y = 2X ^{2}**, the inverse would be

**X = sqrt(Y/2)**. To find the inverse of this equation, you must first switch the x and y values. The inverse will now be

**X**. To solve for x, take the square root of both sides. The resulting equation is

^{2}= Y/2**X = sqrt(Y/2)**.

### Why Does This Work?

The reason why the above equation works to find the inverse of the function is because when the x and y values are switched, the original equation is reversed. This means that if we want to “undo” the function, we must switch the x and y values, and solve for the new x value. To solve for the new x value, we take the square root of both sides, resulting in the equation **X = sqrt(Y/2)**.

### Conclusion

In conclusion, finding the inverse of a nonlinear equation, such as **Y = 2X ^{2}**, can be done by switching the x and y values and then taking the square root of both sides. This results in the equation

**X = sqrt(Y/2)**, which can be used to find the inverse of the original equation.