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

Question

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

Quizplus · Accepted Answer

The expression under the square root, $x^2 - 4$, must be greater than or equal to 0. This expression factors into $(x - 2)(x + 2)$, which is non-negative outside the interval $(-2, 2)$. Thus, the domain includes all $x$ such that $x \leq -2$ or $x \geq 2$, corresponding to $( - \infty , - 2 ] \cup [ 2 , \infty )$.

Find the Domain of X in the Expression x2−4\sqrt { x ^ { 2 } - 4 }x2−4​

Find the Domain of X in the Expression $\sqrt { x ^ { 2 } - 4 }$