find domain if f(x)=sqrt(-2x-6)

Question

I cannot for the life of me figure this problem out and i cannot find an example like this in my math book. Please help! I need to know how to work this problem.

Answer 1

The domain restriction for square (or other even) roots is that the expression under the radical cannot be negative. In this case

-2x-6 ≥ 0

-6 ≥ 2x

-3 ≥ x

Domain: {x | x ≤ -3} in set notation, (-∞, -3] in interval notation