# Question #f690e

Mar 6, 2017

$y = \pm \sqrt{\frac{x + 3}{2}}$

#### Explanation:

Set $\text{ } y = 2 {x}^{2} - 3$

Make $x$ the dependant variable

$y + 3 = 2 {x}^{2}$

Divide both sides be 2

$\frac{y + 3}{2} = {x}^{2}$

Square root both sides

$x = \pm \sqrt{\frac{y + 3}{2}}$

Where there is an $x$ write $y$ and where there is a $y$ write $x$

$y = \pm \sqrt{\frac{x + 3}{2}}$

Note that the inverse function of $f \left(x\right)$ is its reflection about the line $y = x$