Question

Find the inverse of the function f(x)=-2/3x-18 show work

A g(x)=3/2x+27


B g(x)=-3/2x+27


C g(x)=-3/2x-27

D g(x)=3/2x-27

Answer 1

C

let y = f(x)

Then rearrange making x the subject

y = -
`(2)/(3)` x - 18 ( add 18 to both sides )

y + 18 = -
`(2)/(3)` x

multiply both sides by -
`(3)/(2)`

-
`(3)/(2)` (y + 18) = x

x = -
`(3)/(2)` y - 27

change y to x for inverse function

`f^(-1)`(x) = -
`(3)/(2)` x - 27 → C