Keywords:
Function, inverse of a function, variable
To find the inverse of a function we must clear the value of the variable x and finally return change.
By definition we have to:
Be a function of the form [tex]y = f (x)[/tex], the inverse of that function is given by:
[tex]f ^ {- 1} (y) = f ^ {- 1} (x) = x[/tex]
Then we have the following function:
[tex]y = f (x)[/tex]
Where [tex]f (x) = x ^ 2 - 12[/tex]
We clear x:
[tex]x ^ 2 = y + 12[/tex]
[tex]x = \pm\sqrt {y + 12}[/tex]
Returning the change we have:
[tex]f ^ {- 1} (x) = \pm\sqrt {x + 12}[/tex]
Answer:
The inverse function of [tex]y = x ^ 2 - 12[/tex]is [tex]f ^ {- 1} (x) = \pm\sqrt {x + 12}[/tex]
