Question

ASAP! find the inverse of the function y=2x^2+2

a.y=√x-2
b.y=√1/2x-1
c.y=√2x^2-4
d.y=√1/2x-1​

Answer 1

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

Explanation:

We want to find the inverse of the function:

`y=2x^2+2`

To find the inverse of a function, we will flip the variables and solve for y. So:

`x=2y^2+2`

Solve for y. Subtract two from both sides:

`x-2=2y^2`

Divide both sides by two:

`\displaystyle y^2=(1)/(2)x-1`

And take the principal square root of both sides. Therefore:

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