To find the inverse, you need:
1. Switch x and y:
[tex]x = 2y^{2}[/tex]
2. Solve again for y:
[tex] y^{2} = \frac{x}{2}[/tex]
[tex] \left \{ {{y= \sqrt{x/2}} \atop {y = - \sqrt{x/2}}} \right. } [/tex]
This the inverse. The reason why there is two "pieces" is because the first one is the inverse for [tex]y= 2x^{2} [/tex] if [tex]x \geq 0[/tex], and the second one is the inverse for [tex]y = 2 x^{2} [/tex] if [tex]x \leq 0[/tex].
Hope it helps!
