Question

Which equation can be simplified to find the inverse of y = 2x²? O 1/y = 2x² O y = 1/2 x² O -y = 2x² O x = 2y²

Answer 1

the correct equation that can be simplified to find the inverse of
`\( y = 2x^2 \)` is:

`\[ x = 2y^2 \]`

Therefore, option D is correct

To find the inverse of a function, you swap the
`\( x \)` and
`\( y \)` variables and then solve for the new
`\( y \)`. The original function is
`\( y = 2x^2 \)`. Let's go through the steps to find its inverse:

1. Replace
`\( y \)` with
`\( x \)`:
`\( x = 2y^2 \).`

2. Solve for
`\( y \)` to get the inverse function.

We'll proceed with these steps to find the correct equation that can be simplified to find the inverse of the given function.

The steps to find the inverse function yield two potential solutions because the original function is quadratic:

`\[ y = \pm (√(2))/(2) √(x) \]`

However, since the original function
`\( y = 2x^2 \)` only considers the positive square root (as the square of a real number is always non-negative), we take the positive solution for the inverse function:

`\[ y = (√(2))/(2) √(x) \]`

This simplifies to:

`\[ y = \sqrt{(x)/(2)} \]`

Therefore, the correct equation that can be simplified to find the inverse of
`\( y = 2x^2 \)` is:

`\[ x = 2y^2 \]`

This matches the option:

O
`\( x = 2y^2 \)`