How do you get the inverse of f(x) = 3/x+1

To make the typing easier, I'm going to replace f(x) by y:

y  =  3/x + 1

To find its inverse, use this two-step process:

Step 1)  Exchange x and y:  x  =  3/y + 1

Step 2)  Solve for y:      

                  subtract 1 from both sides:  x - 1  =  3/y

                  multiply both sides by y:     (x - 1)y  =  3

                  divide both sides by x - 1:           y  =  3/(x - 1)

This final equation is the inverse.