Final answer:
The domain of the function is all real numbers except the values that make the denominator equal to zero.
Step-by-step explanation:
The question is asking about the domain of the function z=(4x²y⁴-y⁴)/(10xy-6). In this context, the domain refers to the values that the variables x and y can take on. To determine the domain, we need to consider any restrictions or limitations on the values of x and y.
Looking at the function, we can see that the denominator has an expression of 10xy-6. Since division by zero is undefined, we need to ensure that the denominator is not equal to zero. Equating the denominator to zero and solving for x and y will give us the values that are not in the domain.
Therefore, the domain of the function is all real numbers except the values that make the denominator 10xy-6 equal to zero.