Final answer:
The domain of the function (6x) / (x² + 2x - 24) includes all real numbers except for x = -6 and x = 4, where the denominator equals zero.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In the case of the function (6x) / (x² + 2x - 24), the domain is all real numbers except for the values that make the denominator equal to zero, as division by zero is undefined.
We must first factor the denominator to find the values that are not permitted. Factoring x² + 2x - 24 gives (x + 6)(x - 4), which means the function is undefined when x equals -6 or 4. Hence, the domain of the given function is all real numbers except x = -6 and x = 4.