Find the Domain d=v(x^2-x+(y^2-y))*22

Problem

d=v*(x2−x+(y2−y))⋅22

Solution

1. Identify the function type. The expression d=v*(x2−x+y2−y)⋅22 appears to be a multivariable function where v is a function of the expression x2−x+y2−y

2. Determine the constraints. In general mathematical notation, if v represents a square root function (often written as √(,) or v in some contexts), the argument must be non-negative.

3. Set up the inequality. For the function to be defined over the set of real numbers, the expression inside the square root must satisfy:

x2−x+y2−y≥0

4. Complete the square to understand the geometric region. Group the x and y terms:

(x2−x+1/4)+(y2−y+1/4)≥1/4+1/4

5. Simplify the inequality into the standard form of a circle:

(x−1/2)2+(y−1/2)2≥1/2

6. Interpret the result. The domain consists of all points (x,y) in the Cartesian plane that lie on or outside a circle centered at (1/2,1/2) with a radius of √(,1/2)

Final Answer

Domain={(x,y)∈ℝ2:x2−x+y2−y≥0}

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