Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 81 - x ^ { 2 } }$
A) $[ - 81,81 ]$
B) $( - 9,9 )$
C) $[ - 9,81 )$
D) $[ - 9,9 ]$
E) $( - 81,81 )$

Question

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 81 - x ^ { 2 } }$ 
A) $[ - 81,81 ]$
B) $( - 9,9 )$
C) $[ - 9,81 )$
D) $[ - 9,9 ]$
E) $( - 81,81 )$

Quizplus · Accepted Answer

Since we cannot take the square root of a negative number, we need to ensure that the expression inside the square root is non-negative. That is, 
$$81 - x^2 \geq 0 $$ 
Solving this inequality gives $$-9 \leq x \leq 9$$ 
Therefore, the domain of $x$ is $[-9,9]$.

Using a graphing utility, we can graph $y = \sqrt{81-x^2}$ and see that the graph exists only for $x$ values in the interval $[-9,9]$.

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