Question

If f(x)=1/9x-2 , what is f–1(x)?

Answer 1

Lets get started :)

f(x) =
`(1)/(9)x` - 2
y =
`(1)/(9)x` - 2
This is the original equation, and now we have to find the inverse.

When finding the inverse, just flip the variables, x as y and y as x

f ⁻¹(x)
↓
x =
`(1)/(9)y` - 2
We have to isolate y as it is our f ⁻¹(x)

Take 2 to the other side { When you see subtraction, you do addition }
x + 2 =
`(1)/(9) y`

Take 9 to the other side { When you see division, you do multiplication }
9 ( x + 2 ) = y
9x + 18 = y

f ⁻¹ (x) = 9x + 18