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Find the Domain x+2y-x^2-y^4-2xy^2

Problem

x+2*y−x2−y4−2*x*y2

Solution

  1. Identify the type of expression provided. The expression ƒ(x,y)=x+2*y−x2−y4−2*x*y2 is a polynomial function of two variables.

  2. Determine the restrictions for the domain. Polynomials are defined for all real number inputs because they only involve addition, subtraction, and multiplication.

  3. Analyze for potential undefined operations. There are no denominators that could be zero, no square roots of negative numbers, and no logarithms of non-positive numbers.

  4. Conclude that the domain consists of all possible pairs of real numbers (x,y) in the Cartesian plane.

Final Answer

Domain={(x,y)∈ℝ2}

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