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) $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$

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) $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$

Quizplus · Accepted Answer

The expression under 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 the solution $-\frac{3}{2} \leq x \leq \frac{3}{2}$, which corresponds to option C.

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 $\sqrt { 9 - 4 x ^ { 2 } }$