Find the Domain of \(f(x)=\sqrt{9-x^2}\)
Question:
Find the domain of the following real valued function of real variable:
$$
f(x)=\sqrt{9-x^2}
$$
Solution
Given: $$ f(x)=\sqrt{9-x^2} $$
For a square root function, the expression inside the root must be non-negative.
Therefore, $$ 9-x^2\ge0 $$
$$ x^2\le9 $$
$$ -3\le x\le3 $$
Hence, the domain is: $$ [-3,3] $$