Final answer:
The domain of the function y = 3 √(6x + 42) is all real numbers greater than or equal to -7, which is represented as [ -7, ∞ ).
Step-by-step explanation:
The domain of a function is the set of all possible input values (typically 'x' values) for which the function is defined. For the given function y = 3 √(6x + 42), we must consider that the square root function is defined only for non-negative values. Therefore, the expression inside the square root, 6x + 42, must be greater than or equal to zero.
To find the domain, we set up the inequality 6x + 42 ≥ 0. Solving for 'x' gives us x ≥ -7. So, the domain of the function is all real numbers greater than or equal to -7, which can be represented as [ -7, ∞ ).