For this case we must find the inverse of the following function:
[tex]f (x) = x ^ 2-1[/tex]
For them we follow the steps:
We change f (x) to y:
[tex]y = x ^ 2-1[/tex]
We exchange variables:
[tex]x = y ^ 2-1[/tex]
We solve for "y":
[tex]y ^ 2-1 = x[/tex]
We add 1 to both sides of the equation:
[tex]y ^ 2 = x + 1[/tex]
We apply square root to eliminate the exponent:
[tex]y = \pm \sqrt {x + 1}[/tex]
We change y by [tex]f ^ {- 1} (x)[/tex]:
[tex]f ^ {- 1} (x) =\pm \sqrt {x + 1}[/tex]
Answer:
Option D
