Question

Which equation can be simplied to find the inverse of y=2xsquared

Answer 1

The inverse of the function y = 2x2 is found by switching x and y and solving for the new y, leading to y = ±√(x/2). Since the original function is a parabola with positive y-values, the negative root is disregarded, and the inverse is y = √(x/2).

To find the inverse of the given function
`\(y = 2x^2\)`, you can follow these steps:

Step 1: Replace y with x and x with y:

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

Step 2: Solve for y:

`\[ (x)/(2) = y^2 \]`

Step 3: Take the square root of both sides:

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

So, the inverse function is
`\(y = \pm\sqrt{(x)/(2)}\)`.