Find the domain of the function. \[ g(x)=\sqrt{-x}-2 \] Write your answer using interval notation.

Step 1 ：The function is given as \(g(x)=\sqrt{-x}-2\).

Step 2 ：The domain of a function is the set of all possible input values (x-values) which will produce a valid output.

Step 3 ：For this function, we need to find all x-values for which the function is defined.

Step 4 ：The function is a square root function. The square root of a number is only defined for non-negative numbers.

Step 5 ：Therefore, the expression inside the square root, -x, must be greater than or equal to 0.

Step 6 ：So, we need to solve the inequality -x >= 0.

Step 7 ：The solution to the inequality -x >= 0 is x <= 0.

Step 8 ：This means that the function g(x) is defined for all x-values less than or equal to 0.

Step 9 ：In interval notation, this is written as (-∞, 0].

Step 10 ：Final Answer: The domain of the function is \(\boxed{(-\infty, 0]}\).