The domain of the function `f(x)=sqrt(2-2x-x^2)` is
`[-sqrt(3),\ sqrt(3)]` b. `[-1-sqrt(3),\ -1+sqrt(3)]` c. `[-2,2]` d. `[-2-sqrt(3),-2+sqrt(3)]`

Explanation

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

\[ 2 - 2x - x^2 \geq 0 \]

### Step 1: Rearranging the Inequality
First, we rearrange the inequality:
...