Answer:
[tex]\displaystyle y=\sqrt{\frac{1}{2}x -1}[/tex]
Step-by-step explanation:
We want to find the inverse of the function:
[tex]y=2x^2+2[/tex]
To find the inverse of a function, we will flip the variables and solve for y. So:
[tex]x=2y^2+2[/tex]
Solve for y. Subtract two from both sides:
[tex]x-2=2y^2[/tex]
Divide both sides by two:
[tex]\displaystyle y^2=\frac{1}{2}x-1[/tex]
And take the principal square root of both sides. Therefore:
[tex]\displaystyle y=\sqrt{\frac{1}{2}x -1}[/tex]
