Find the Domain 3x+2y-z=3

Problem

3*x+2*y−z=3

Solution

1. Identify the type of equation provided. The equation 3*x+2*y−z=3 represents a linear equation in three variables, which geometrically describes a plane in three-dimensional space ℝ3

2. Determine if there are any restrictions on the variables. In a linear polynomial equation, there are no square roots of negative numbers, no denominators that could be zero, and no logarithmic arguments that must be positive.

3. Conclude the domain based on the lack of restrictions. Since the expression is defined for all real values of x y and z the domain is the set of all ordered triples in three-dimensional real space.

Final Answer

Domain={[(x,y,z),x,y,z∈ℝ]}

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