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

Question

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

Quizplus · Accepted Answer

For the expression to be defined, the radicand must be non-negative. This means that $25-x^2\geq0$, or $-5\leq x\leq 5$. Therefore, the domain of $x$ is $[-5,5]$. To verify this, we can graph $y=\sqrt{25-x^2}$ on a graphing utility and see that the graph only exists for $x$ values in the interval $[-5,5]$.

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

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