fx=3x+2 -1 f^-1x=

To find the inverse of the function f(x), we need to switch the roles of x and y and solve for y.

Let y = f(x) = 3/(x+2) - 1

Switching the roles of x and y, we get:

x = 3/(y + 2) - 1

To solve for y, we can isolate y on one side of the equation:

x + 1 = 3/(y + 2)

Multiply both sides by (y + 2):

(x + 1)(y + 2) = 3

Expand the left side:

xy + 2x + y + 2 = 3

Rearrange the terms:

xy + y = 3 - 2x - 2

Combine like terms:

xy + y = 1 - 2x

Factor out y:

y(x + 1) = 1 - 2x

Divide both sides by (x + 1):

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

Therefore, the inverse of f(x) = 3/(x+2) - 1 is f^(-1)(x) = (1 - 2x)/(x + 1)