Find the Domain z=x^3+y^3-9xy+27

Problem

z=x^3+y^3−9*x*y+27

Solution

1. Identify the type of function provided. The expression z=x^3+y^3−9*x*y+27 is a polynomial function of two variables, x and y

2. Determine if there are any restrictions on the variables. Polynomials are defined for all real numbers because they do not involve division by zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. State the domain in terms of the possible values for x and y Since there are no restrictions, the domain consists of all ordered pairs (x,y) in the two-dimensional real plane.

Final Answer

Domain={(x,y)∈ℝ^2}

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