Find the Domain z=4x-4y-x^2-y^2

Problem

z=4*x−4*y−x2−y2

Solution

1. Identify the type of function provided. The expression z=4*x−4*y−x2−y2 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 number inputs because they do not involve division by zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Conclude that the domain consists of all possible ordered pairs (x,y) in the two-dimensional real plane.

Final Answer

Domain:{(x,y)|x∈ℝ,y∈ℝ}

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