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
#x -2 = 0 implies x = 2#
so this value of
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
#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
#x in (-oo, 0] uu (2, + oo)#
graph{sqrt(x/(x-2)) [-10, 10, -5, 5]}