Question

Given the function f(x) = 3 (x - 9) + 6 which of the following represents f-1 (x)?

Answer 1

`f^(-1)`(x) =
`(1)/(3)` x + 7

Explanation:

let y = f(x) and rearrange making x the subject, that is

y = 3(x - 9) + 6 ← distribute and simplify right side

y = 3x - 27 + 6 = 3x - 21 ( add 21 to both sides )

y + 21 = 3x ( divide all terms by 3 )

`(1)/(3)` y + 7 = x

Change y back into terms of x with x =
`f^(-1)`(x) , thus

`f^(-1)`(x) =
`(1)/(3)` x + 7