Find the Domain x-6y+4z=-12

Problem

x−6*y+4*z=−12

Solution

1. Identify the type of equation provided. The equation x−6*y+4*z=−12 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 logarithms of non-positive numbers.

3. Conclude the domain based on the lack of constraints. 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)∈ℝ3}

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