Question

If f(x) = 1/9x-2, what is f-1(x)?

Answer 1

`\int\limits^ {-1} \, (x) = 9x +18`

Explanation:

We must find the inverse of the following function:

`\int\limits {x} =`
`(1)/(9)x - 2`

to solve this, you change f(x) by y

y=
`(1)/(9) x - 2`

exchange the variables:

`x(1)/(9)y - 2`

You clear the variable "y"

`x+ 2 = (1)/(9)y`

9(x+2) = y

y = 9(x+2)

y = 9x +18

finally you change "y" to f ^-1 (x) =

f^-1 (x) = 9x+18