Question

What is the inverse function of y=2x^2+2

Answer 1

The answer is

`y = \pm\sqrt{ (1)/(2)x - 1 }`

Explanation:

`y = {2x}^(2) + 2`

Interchange the terms

That's x becomes y and y becomes x

`x = {2y}^(2) + 2`

Next solve for y

Send 2 to the other side of the equation

`{2y}^(2) = x - 2`

Divide both sides by 2

`\frac{ {2y}^(2) }{2} = (x - 2)/(2) \\ {y}^(2) = (x)/(2) - (2)/(2) \\ {y}^(2) = (1)/(2) x - 1`

Find the square root of both sides to make y stand alone

That's

`\sqrt{ {y}^(2) } = \sqrt{ (1)/(2)x - 1 }`

We have the final answer as

`y = \pm\sqrt{ (1)/(2)x - 1 }`

Hope this helps you