Question 1208167
<font color=black size=3>
f(x) = (x+2)/(x-2)
y = (x+2)/(x-2)
x = (y+2)/(y-2) .... swap x and y; solve for y
x(y-2) = y+2
xy-2x = y+2
xy-y = 2+2x
y(x-1) = 2x+2
y = (2x+2)/(x-1)
g(x) = (2x+2)/(x-1)


g(x) is the inverse of f(x), and vice versa.
To verify, you need to show that, 
f( g(x) ) = x and g( f(x) ) = x
for all x in the domain. I'll leave this verification for the student to do.
</font>