Question

Given f(x) = 6x - 4 / 2x + 1 find the inverse function , f ^ - 1 (x) ,
f ^ - 1 (x) =

Answer 1

`f^(-1)`(x) = -
`(4+x)/(2x-6)`

let y =
`(6x-4)/(2x+1)`

rearrange making x the subject, begin by cross-multiplying

y(2x + 1) = 6x - 4

2xy + y = 6x - 4

collect terms in x together

2xy - 6x = - 4 - y

x(2y - 6) = - (4 + y ) ( divide both sides by (2y - 6) )

x =
`(-(4+y))/(2y-6)`

change y back to x for inverse

`f^(-1)`(x) = -
`(4+x)/(2x-6)`