Find the Domain x+2y-z=0

Problem

x+2*y−z=0

Solution

1. Identify the type of equation provided. The equation x+2*y−z=0 represents a plane in three-dimensional space ℝ3

2. Analyze the variables for restrictions. The expression is a linear polynomial involving x y and z

3. Determine if there are any operations that would restrict the domain, such as division by zero, square roots of negative numbers, or logarithms of non-positive numbers.

4. Conclude that since there are no such operations, the variables x y and z can take any real value.

5. Express the domain as the set of all ordered triples in three-dimensional real space.

Final Answer

Domain=ℝ3

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