Question

Find f^-1(x) where
f(x) = 3x+2/x

Answer 1

Given:

Consider the function is

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

To find:

The inverse of the function, .i.e.,
`f^(-1)(x)`.

Solution:

We have,

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

Putting f(x)=y, we get

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

Isolate the variable y.

`xy=3y+2`

`xy-3y=2`

`y(x-3)=2`

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

Putting
`y=f^(-1)(x)`, we get

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

Therefore, the inverse function is
`f^(-1)(x)=(2)/(x-3)`.