Question

Given f(x) = ax – b, what is f-1(x)?

Answer 1

x + b/a Replace f(x) with y, interchange x and y and solve for y.

Answer 2

`f^(-1)` (x) =
`(x+b)/(a)`

Explanation:

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

y = ax - b ( add b to both sides )

y + b = ax ( divide both sides by a )

`(y+b)/(a)` = x

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

`f^(-1)` (x) =
`(x+b)/(a)`