For this case we must find the inverse of the following function:
[tex]f (x) = \frac {1} {9} x-2[/tex]
To do this, we follow the steps below:
We change[tex]f (x)[/tex]by y:
[tex]y = \frac {1} {9} x-2[/tex]
We exchange the variables:
[tex]x = \frac {1} {9} y-2[/tex]
We clear the variable "y":
[tex]x + 2 = \frac {1}{9} y\\9 (x + 2) =y\\y = 9 (x + 2)\\y = 9x + 18[/tex]
Finally, we change "y" to[tex]f^{-1}(x):[/tex]
[tex]f^{-1}(x) = 9x + 18[/tex]
ANswer:
The inverse of the given function is:[tex]f^{-1}(x) = 9x + 18[/tex]
