Question

Find the inverse of the function y = 2x² + 2.

Answer 1

To find the inverse of the function y = 2x² + 2, swap the x and y variables and solve for the new y. The inverse function is y = √((x - 2)/2).

Step-by-step explanation:

To find the inverse of the function y = 2x² + 2, we need to swap the x and y variables and solve for the new y. Let's start:

1. Replace y with x and x with y: x = 2y² + 2
2. Subtract 2 from both sides: x - 2 = 2y²
3. Divide both sides by 2: (x - 2)/2 = y²
4. Take the square root of both sides: √((x - 2)/2) = y

So, the inverse of the function is y = √((x - 2)/2).