Question

F(x)=2x-4. F(x)=2x-4 f-1x=_x+_. Complete the inverse function

Answer 1

`f^(-1)(x) = (1)/(2)(x +4)`

Explanation:

Given

`f(x) = 2x - 4`

Required

Determine the inverse function

Start by replacing f(x) with y

`y = 2x - 4`

Swap the positions of y and x

`x = 2y - 4`

Make y the subject: Add 4 to both sides

`x+4 = 2y - 4+4`

`x+4 = 2y`

Make y the subject: Divide through by 2

`(1)/(2)(x + 4) = y`

`y = (1)/(2)(x + 4)`

Replace y with f-1(x)

`f^(-1)(x) = (1)/(2)(x +4)`