Choose the inverse of y=X2-2

Question

asked Jun 6, 2020 160k views

2 Answers

Irineu Antunes · Answer 1 · 2020-06-11T15:46:26+0000

For this case we must find the inverse of the following function:

y = x ^ 2-2

We exchange the variables:

x = y ^ 2-2

We clear the variable "y":

Adding 2 to both sides we have:

x + 2 = y ^ 2

Applying square root on both sides of the equation:

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

We change y by
$f ^ {- 1} (x)$ :
$f ^ {- 1} (x) =\pm \sqrt {x + 2}$

Answer:

$f ^ {- 1} (x) = \pm\sqrt {x + 2}$