Here, so its domain is all real numbers except 1. which has domain .
The domain of fog will be all x, except 1, such that . If x> 1, x-1> 0 so, multiplying on both sides by the positive number x- 1, or . If x< 1, x- 1< 0 so, multiplying both sides by the negative number x- 1, or . Of course, we can't have "x< 1" and " " so that last case is impossible. We must have x> 1 and as you say.