For this case we must find the inverse of the following function:
[tex]y = x ^ 2-2[/tex]
We exchange the variables:
[tex]x = y ^ 2-2[/tex]
We clear the variable "y":
Adding 2 to both sides we have:
[tex]x + 2 = y ^ 2[/tex]
Applying square root on both sides of the equation:
[tex]y = \pm \sqrt {x + 2}[/tex]
We change y by [tex]f ^ {- 1} (x)[/tex]:[tex]f ^ {- 1} (x) =\pm \sqrt {x + 2}[/tex]
Answer:
[tex]f ^ {- 1} (x) = \pm\sqrt {x + 2}[/tex]
