Answer: The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
The square root function is defined for non-negative numbers, so the expression inside the square root must be non-negative.
In this case, -6x - 7 must be greater or equal to 0.
-6x - 7 ≥ 0
x ≥ (7 + 7)/6 = 14/6 = 7/3
So the domain of the function is x ≥ 7/3, or x ∈ [7/3, ∞)
In interval notation, the domain of f(x) = √-6x - 7 is x ∈ [7/3, oo)
Explanation: