Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - 16 x ^ { 2 } }$
A) $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
B) $\left[ - \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right]$
C) $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$
D) $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
E) $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$

Question

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 25 - 16 x ^ { 2 } }$ 
A) $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
B) $\left[ - \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right]$
C) $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$
D) $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
E) $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$

Quizplus · Accepted Answer

The expression under the square root, $25 - 16x^2$, must be greater than or equal to 0 for the square root to be defined. Solving the inequality $25 - 16x^2 \geq 0$ gives the domain of $x$ as $[- \frac { 5 } { 4 } , \frac { 5 } { 4 }]$.

Find the Domain Of xxx In the Expression 25−16x2\sqrt { 25 - 16 x ^ { 2 } }25−16x2​

Find the Domain Of $x$ In the Expression $\sqrt { 25 - 16 x ^ { 2 } }$