Question

Let f(x)=2/3x-6 what is the inverse function?

Answer 1

Change f(x) to a y and switch places with y and x as below.

`x= (2)/(3) y-6`

Solve the equation for y

`x + 6 = (2)/(3) y`

Multiply each term by the reciprocal of
`(2)/(3)`

`(3)/(2) (x+6) = y`

Distribute

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

Change y to
`f^(-1)(x)`

`f^(-1)(x)= (3)/(2) x+9`