Let f/left (x/right) = / frac{2}{x}f (x) = 2 x and g/left (x/right) = / frac{x}{x-1}g (x) = x x - 1. Find the domain of / left (/frac{f}{g}/right) / left (x/right) (f g) (x). Group of answer choices

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, + ∞).