Find the Domain of the Function
Question:
Domain of
\[ f(x)=\sqrt{a^2-x^2}, \qquad a>0 \]
is
(a) \(( -a,a)\)
(b) \([ -a,a]\)
(c) \([0,a]\)
(d) \(( -a,0]\)
Solution:
For square root function,
\[ a^2-x^2\ge0 \]
\[ x^2\le a^2 \]
\[ -a\le x\le a \]
Therefore, domain is
\[ \boxed{[-a,a]} \]
\[ \boxed{\text{Correct Answer: (b)}} \]