Question

If f(x) = 1/9 x-2 , what is f–1(x)?

Answer 1

Hello,

y=1/9 x-2
==>x=1/9 y -2
==>9x=y-18
==>y=9x+18

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

Answer 2

`f^(-1)(x)=9x+2`

Explanation:

Given:
`f(x)=(1)/(9)(x-2)`

We need to find the inverse of f(x).

Step 1: Set f(x) = y

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

Step 2: Switch x and y

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

Step 3: Solve for y, Isolate y

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

Multiply by 9 both sides

`9x=y-2`

Add 2 both sides

`9x+2=y`

`y=f^(-1)(x)`

Hence,
`f^(-1)(x)=9x+2`