Composition of functions; what is the domain

f(x)= x/x+1 and g(x)= 1/x-2
Find the domain of f(g(x))

Is this right? :s
f(g(x))= 1/x-1
Domain of g(x)= (-inf, 2) U (2, +inf)
Domain of f(x)= (-inf, -1) U (-1, +inf)
Therefore g(x) cannot be -1
I solved g(x)= -1 and got 1 so wouldn't the domain of f(g(x)) be (-inf, 1) U (1,2) U (2, +inf) ?!

Yes, I agree with you!
f(g(x)) is all reals, except x cannot equal 1, or 2, which is what you have.
Very nice work.