Final answer:
The domain of the function cos(x-6/y³) is all values of x and y that make y³ not equal to zero.
Step-by-step explanation:
The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is cos(x-6/y³). To find the domain, we need to consider any restrictions on the input variables x and y.
The only restriction we have here is that the denominator y³ cannot be equal to zero, as division by zero is undefined. So, the domain of the function is all values of x and y that make y³ not equal to zero.