Question

What is the inverse of the function f(x) = 2x + 1?

h(x) = 1/2x – 1/2
h(x) = 1/2x + 1/2
h(x) = 1/2x – 2
h(x) =1/2 x + 2

Answer 1

h(x) =
`(1)/(2)` x -
`(1)/(2)`

Explanation:

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

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

`(y-1)/(2)` = x

change y back to x with x the inverse function h(x)

h(x) =
`(x-1)/(2)` =
`(1)/(2)` x -
`(1)/(2)`