Question

Find the inverse of y=2x^2

Answer 1

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