Find the Domain 1/4x-y=6

Problem

1/(4*x−y)=6

Solution

1. Identify the restriction for the expression. In a rational equation, the denominator cannot be equal to zero because division by zero is undefined.

2. Set the denominator equal to zero to find the values that must be excluded from the domain.

denominator=4*x−y

4*x−y=0

3. Solve for one variable to express the restriction. Adding y to both sides gives the condition for the undefined points.

y=4*x

4. Define the domain as the set of all ordered pairs (x,y) such that the denominator is not zero.

{(x,y)∈ℝ2|y≠4*x}

Final Answer

Domain:{(x,y)|y≠4*x}

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