Find the Domain 4x-y+z=2

Problem

4*x−y+z=2

Solution

1. Identify the type of equation provided. The equation 4*x−y+z=2 represents a plane in three-dimensional space, which is a linear function of two independent variables.

2. Express the equation in terms of a dependent variable, typically z to view it as a function z=ƒ(x,y)

z=2−4*x+y

3. Analyze the expression for any restrictions. The expression $2 - 4x + y$ is a polynomial. Polynomials do not have denominators that could be zero, square roots of negative numbers, or logarithms of non-positive numbers.

4. Determine the domain. Since there are no mathematical restrictions on the values that x and y can take, the domain consists of all possible ordered pairs (x,y) in the real coordinate plane.

5. State the domain using set-builder notation or interval notation for the variables.

Final Answer

Domain={(x,y)|x∈ℝ,y∈ℝ}

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