Question

What is the inverse function of `f(x) = (2x)/(x+3)`?

Answer 1

`f^-1(x)=(-3x)/(x-2)`

Explanation:

`f(x)=y=(2x)/(x+3)`
`xy+3y=2x`
`xy-2x=-3y`
`x(y-2)=-3y`
`x=(-3y)/(y-2)=f^-1(y)`
`f^-1(x)=(-3x)/(x-2)`

Answer 2

`f^-1(x)=-(3x)/(x-2)`

Explanation:

`"Rearrange making x the subject"`

`y=(2x)/(x+3)`

`rArry(x+3)=2x`

`rArrxy+3y=2x`

`rArrxy-2x=-3y`

`rArrx(y-2)=-3y`

`rArrx=-(3y)/(y-2)`

`"change y into x and we have the inverse"`

`rArrf^-1(x)=(3x)/(x-2)`