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) $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$
C) $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$
D) $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
E) $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$

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) $\left[ - \frac { 4 } { 5 } , - \frac { 4 } { 5 } \right]$
C) $\left[ - \frac { 4 } { 5 } , \frac { 4 } { 5 } \right]$
D) $\left[ \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$
E) $\left[ - \frac { 5 } { 4 } , \frac { 5 } { 4 } \right]$

Quizplus · Accepted Answer

The expression is defined when the radicand is nonnegative, so $25 - 16x^2 \ge 0$. Solving this inequality gives $- \frac{5}{4} \le x \le \frac{5}{4}$.

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 $\sqrt { 25 - 16 x ^ { 2 } }$