Find the Domain (x+y-z)=0

Problem

x+y−z=0

Solution

1. Identify the type of equation. The expression x+y−z=0 represents a linear equation in three variables, which defines a plane in three-dimensional space ℝ3

2. Analyze the constraints. There are no square roots of negative numbers, no logarithms of non-positive numbers, and no divisions by zero within the expression.

3. Determine the domain. Since the variables x y and z can take any real value without violating any mathematical rules, the domain for each variable is the set of all real numbers.

4. Express the domain in set notation. The domain is the set of all ordered triples (x,y,z) in ℝ3 that satisfy the given equation.

Final Answer

Domain={[(x,y,z)∈ℝ3,x+y−z=0]}

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