The domain of the function `f(x)=sqrt(5|x|-x^2-6)` is (a) `(-3,\ -2)uu(2,3)` b. `[-3,-2)uu[2,3)` c. `[-3,-2]uu[2,3]` d. none of these

Explanation

To find the domain of the function \( f(x) = \sqrt{5|x| - x^2 - 6} \), we need to ensure that the expression inside the square root is non-negative. This means we need to solve the inequality:

\[ 5|x| - x^2 - 6 \geq 0 \]

### Step 1: Analyze the absolute value

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