Question

Find the inverse of the function. y = 2x2 –4

Answer 1

To find inverse functions, switch the two variable and solve for y:

x=2y²-4
x+4=2y²
(x+4)/2=y²
√((x+4)/2)=y

Answer 2

The inverse function is
`y=\sqrt{(x+4)/(2)}`

Explanation:

The given function is
`y=2x^2-4`.

This function is only invertible on the interval,
`x\ge 0`.

To find the inverse on this interval, we interchange
`x` and
`y`.

`x=2y^2-4`

We now make
`y` the subject to get,

`x+4=2y^2`

`\Rightarrow (x+4)/(2)=y^2`

`\Rightarrow \pm \sqrt{(x+4)/(2)}=y`

But the given interval is
`x\geq 0`, This implies that,
`y\geq 0`.

`y=\sqrt{(x+4)/(2)}`