Final answer:
The domain of the function f(x) = -√(5 - x) - 3 is all real numbers less than or equal to 5, which is expressed as (-∞, 5].
Step-by-step explanation:
To find the domain of the function f(x) = -√(5 - x) - 3, we must identify all the values of x for which the function is defined.
The square root function is only defined for non-negative numbers.
Therefore, the expression inside the square root, 5 - x, must be greater than or equal to zero.
To find these values, we set up the inequality 5 - x ≥ 0.
Solving for x, we get x ≤ 5.
This means that x can be any real number up to and including 5.
So, the domain of the function is (-∞, 5].