Final answer:
The domain of the function f(x)= √(-4-2x) is all real numbers less than or equal to -2.
Step-by-step explanation:
The domain of the function f(x)= √(-4-2x) is the set of all real numbers that make the expression under the square root valid. To find the domain, we set the expression inside the square root to be greater than or equal to zero and solve for x:
-4-2x ≥ 0
Adding 4 to both sides of the inequality, we get:
-2x ≥ 4
Dividing both sides of the inequality by -2 (remember to flip the inequality sign), we get:
x ≤ -2
So, the domain of the function is all real numbers less than or equal to -2, written as:
-∞, -2]