Question

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

Answer 1

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, +∞).