Final answer:
The domain of the function f(x) = 15 - sqrt(x+2) is all real numbers greater than or equal to -2, expressed as [{-2}, ∞).
Step-by-step explanation:
To find the domain of the function f(x) = 15 - sqrt(x+2), we need to determine the set of all real numbers x that make the expression under the square root, x+2, non-negative. This is because the square root of a negative number is not a real number, and our function is defined only over the real numbers.
The condition for the expression under the square root to be non-negative is x+2 ≥ 0. Solving this inequality gives us x ≥ -2. Therefore, the domain of the function is all real numbers greater than or equal to -2.
In mathematical notation, we express the domain as: [{-2}, ∞), where the square bracket indicates that -2 is included in the domain, and the infinity symbol shows that the domain extends to all greater real numbers without bound.