Find the Domain x-2y+z=8

Problem

x−2*y+z=8

Solution

1. Identify the type of equation provided. The equation x−2*y+z=8 represents a plane in three-dimensional space, which is a linear function of three variables.

2. Determine the independent variables. In the context of a function z=ƒ(x,y) we can rewrite the equation to express z in terms of x and y

3. Solve for z to see the functional form.

z=8−x+2*y

4. Analyze the expression for restrictions. The expression 8 - x + 2y$ is a polynomial. Polynomials have no square roots of negative numbers, no divisions by zero, and no logarithms of non-positive numbers.

5. Conclude the domain. Since there are no mathematical restrictions on the values that x or y can take, the domain consists of all real number pairs (x,y) in ℝ2

Final Answer

Domain={(x,y)|x∈ℝ,y∈ℝ}

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