Answer:
The domain is (-∞,0) ∪ (0,1) ∪ (1, +∞)
Step-by-step explanation:
In order to be able to compute f/g (x), we need that x is on the domain of f and in the domain of g.
f(x) = 2/x
In order to be able to compute f(x), we need that the denominator is different from 0, hence x≠0.
g(x) = x/x-1
In order to be able to compute g(x). we need x-1 to be different from 0, thus x≠1.
We also need the denominator of f/g (x) to be different from 0, hence g(x) ≠ 0. In order for g(x) = x/x-1 to be 0, the numerator x should be 0, as a result, we need x≠0 in order to have g(x) ≠ 0.
The domain of f/g (x) is every real nummber besides 0 and 1, in other words, it is (-∞,0) ∪ (0,1) ∪ (1, +∞).
