Find the Domain z=x^2+y^2

Problem

z=x2+y2

Solution

1. Identify the type of function provided. The expression z=x2+y2 is a multivariable polynomial function (specifically a quadratic form) where z depends on two independent variables, x and y

2. Check for mathematical restrictions. Common restrictions include division by zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Determine the constraints for x and y Since squaring any real number is a well-defined operation and there are no denominators or radicals, x and y can be any real numbers.

4. Express the domain in set notation. The domain consists of all ordered pairs (x,y) in the two-dimensional real plane.

Final Answer

Domain={(x,y)∈ℝ2}

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