x will be in the domain of fog if it is in the domain of gandg(x) is in the domain of f.

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.