Find the domain of the function.
$$g ( x ) = \sqrt { 25 - x ^ { 2 } }$$
A) $- 5 \leq x \leq 5$
B) $x \leq - 5$ or $x \geq 5$
C) $x \geq 0$
D) $x \leq 5$
E) all real numbers

Question

Quizplus · Accepted Answer

The function $\sqrt{25-x^2}$ is defined only for values of $x$ that make the expression $25-x^2$ non-negative, otherwise the square root would not be real. So, we solve the inequality $25-x^2\geq 0$:
\begin{align*}
25-x^2&\geq 0\
x^2&\leq 25\
-5\leq x&\leq 5
\end{align*}
Therefore, the domain of the function is $-5\leq x\leq 5$, which means that the best choice is $\boxed{	extbf{(A)}}$.

Find the Domain of the Function g(x)=25−x2g ( x ) = \sqrt { 25 - x ^ { 2 } }g(x)=25−x2​

Find the Domain of the Function $g ( x ) = \sqrt { 25 - x ^ { 2 } }$