Find the domain of x in the expression. $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$
A) $( - 4,0 ] \cap ( 6 , \infty )$
B) $( - 6,0 ] \cup ( 4 , \infty )$
C) $( - 4,0 ] \cup ( 6 , \infty )$
D) $( - 4,0 ] \cup ( - 6 , \infty )$
E) $( - 6,0 ] \cap ( - 4 , \infty )$

Question

Find the domain of x in the expression.​ $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$ ​
A) $( - 4,0 ] \cap ( 6 , \infty )$
B) $( - 6,0 ] \cup ( 4 , \infty )$
C) $( - 4,0 ] \cup ( 6 , \infty )$
D) $( - 4,0 ] \cup ( - 6 , \infty )$
E) $( - 6,0 ] \cap ( - 4 , \infty )$

Quizplus · Accepted Answer

The expression under the square root, $\frac{x}{x^2 - 2x - 24}$, must be greater than or equal to 0. Factoring the denominator gives $x^2 - 2x - 24 = (x - 6)(x + 4)$. The critical points are x = -4 and x = 6. Testing intervals around these points, we find that the expression is positive for $x \in (-4, 0]$ and $x \in (6, \infty)$. Thus, the domain is the union of these intervals, which is option C.

Find the Domain of X in the Expression xx2−2x−24\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }x2−2x−24x​​

Find the Domain of X in the Expression $\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$