Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$
A) $( - 36,0 ] \cup ( 36 , \infty )$
B) $( - 36,0 ] \cap ( 36 , \infty )$
C) $( - 36,0 ] \cap ( 6 , \infty )$
D) $( - 6,0 ] \cup ( 6 , \infty )$
E) $( - 36,0 ] \cap ( - 6 , \infty )$

Question

Find the domain of x in the expression.​ $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$ ​
A) $( - 36,0 ] \cup ( 36 , \infty )$
B) $( - 36,0 ] \cap ( 36 , \infty )$
C) $( - 36,0 ] \cap ( 6 , \infty )$
D) $( - 6,0 ] \cup ( 6 , \infty )$
E) $( - 36,0 ] \cap ( - 6 , \infty )$

Quizplus · Accepted Answer

The expression under the square root, $\frac{x}{x^2-36}$, must be greater than or equal to 0. The denominator $x^2-36$ factors to $(x+6)(x-6)$, which is zero at $x = -6$ and $x = 6$, creating intervals to test for the sign of the expression. The numerator $x$ changes sign at $x=0$. Considering the intervals and the requirement that the denominator must not be zero, the domain is $(-6,0] \cup (6, \infty)$.

Find the Domain of X in the Expression xx2−36\sqrt { \frac { x } { x ^ { 2 } - 36 } }x2−36x​​

Find the Domain of X in the Expression $\sqrt { \frac { x } { x ^ { 2 } - 36 } }$