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\rig ht)( 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, +∞).

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.