Find the Domain x-3y+5z=14

Problem

x−3*y+5*z=14

Solution

1. Identify the type of equation provided. The equation x−3*y+5*z=14 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 expression, 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 based on the lack of restrictions. Since the expression is defined for all real values of x y and z the domain consists of all ordered triples in the three-dimensional real coordinate space.

Final Answer

Domain={[(x,y,z),x,y,z∈ℝ]}

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