# How do you find the domain of #sqrt((x/(x-2)))#?

##### 1 Answer

#### Explanation:

The first thing to look out for is any value of **zero**. That happens when

#x -2 = 0 implies x = 2#

so this value of *excluded* from the domain of the function.

The second thing to look out for is the fact that you're dealing with a *square root*, which, for **real numbers**, can only be taken of *positive numbers*.

This means that the fraction **must be** greater than or equal to **zero**.

#x/(x-2) >= 0 #

This condition is satisfied for

#x <= 0 implies {(x <=0), (x-2 < 0) :} implies x/(x-2) >=0#

and

#x >2 implies {( x>2), (x - 2 > 0) :} implies x/(x-2) >= 0#

Therefore, the domain of the function will include any value of *smaller than or equal to* *greter* than

#x in (-oo, 0] uu (2, + oo)#

graph{sqrt(x/(x-2)) [-10, 10, -5, 5]}