Find the domain of x in the expression.
$\sqrt { 9 - 4 x ^ { 2 } }$
A) $\left[ \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$
B) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$
C) $\left[ - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$.
D) $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$
E) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$.

Question

Find the domain of x in the expression.
 $\sqrt { 9 - 4 x ^ { 2 } }$  
A) $\left[ \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$
B) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$
C) $\left[ - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$.
D) $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$
E) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$.

Quizplus · Accepted Answer

The expression inside the square root, $9 - 4x^2$, must be greater than or equal to 0 for the square root to be defined. Solving the inequality $9 - 4x^2 \geq 0$ gives $x^2 \leq \frac{9}{4}$, which means $x$ must be in the range $[- \frac{3}{2}, \frac{3}{2}]$.

Find the Domain of X in the Expression 9−4x2\sqrt { 9 - 4 x ^ { 2 } }9−4x2​

Find the Domain of X in the Expression $\sqrt { 9 - 4 x ^ { 2 } }$