The domain of the function $f ( x ) = \sqrt { x ^ { 2 } - 4 }$ is

A) $( - \infty , \infty )$
B)(-2,2)
C) $[ - 2,2 ]$
D) $( - \infty , - 2 ) \cup ( 2 , \infty )$
E) $( - \infty , - 2 ] \cup [ 2 , \infty )$

Question

The domain of the function $f ( x ) = \sqrt { x ^ { 2 } - 4 }$ is

A) $( - \infty , \infty )$
B)(-2,2)
C) $[ - 2,2 ]$
D) $( - \infty , - 2 ) \cup ( 2 , \infty )$
E) $( - \infty , - 2 ] \cup [ 2 , \infty )$

Quizplus · Accepted Answer

The expression inside the square root, $x^2 - 4$, must be non-negative. Solving $x^2 - 4 \geq 0$ gives $x \leq -2$ or $x \geq 2$. Thus, the domain is $(-\infty, -2] \cup [2, \infty)$.

The Domain of the Function f(x)=x2−4f ( x ) = \sqrt { x ^ { 2 } - 4 }f(x)=x2−4​

The Domain of the Function $f ( x ) = \sqrt { x ^ { 2 } - 4 }$