Show that the given functions are inverse functions or not g

Show that the given functions are inverse functions or not

g(x) = -3x-2 / x-1

g(x) = (-3x -2)/(x -1)

y = (-3x -2)/(x -1)

In verse of g(x) :

Plug x= y and y = x and solve for y:

y = (-3x -2)/(x -1)

x = ( -3y -2)/( y -1)

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

xy -x = -3y -2

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

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

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