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

Question

asked Jul 20, 2019 45.9k views

2 Answers

Cerron · Answer 1 · 2019-07-26T04:06:28+0000

Answer:

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
and
.

x=2y^2-4

We now make
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,
$y\geq 0$ .

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