Given f(x) = (1/x + 2) + 3, find the inverse function.

MY WORK:

Let y = f(x).

y = (1/x + 2) + 3

Switch x and y.

x = (1/y + 2) + 3

Multiply both sides by (y+2).

I ended up with

xy + 2x = 3y + 7

I then subtracted 3y and 2x from both sides.

xy - 3y = -2x + 7

I factored out a y from the left side.

y(x - 3) = -2x + 7

I finally divided both sides by (x - 3).

y = (-2x + 7)/(x - 3)

Then y becomes f^(-1) x

f^(-1) x = (-2x + 7)/(x - 3)

Is the right?