Find the Domain 3x-2y-2z=-1

Problem

3*x−2*y−2*z=−1

Solution

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

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

3. Conclude the domain. Since the expression is defined for all real values of x y and z the domain consists of all ordered triples (x,y,z) in the set of real numbers.

Final Answer

Domain={(x,y,z)|x,y,z∈ℝ}

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