Find the Domain 1/3x-1/4y-2

Problem

1/(3*x−1/4*y−2)

Solution

1. Identify the restriction for a rational expression. A fraction is defined only when its denominator is not equal to zero.

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

3*x−1/4*y−2=0

3. Solve for one variable, such as y to describe the relationship between x and y that results in an undefined expression.

−1/4*y=−3*x+2

4. Multiply both sides by −4 to isolate y

y=12*x−8

5. State the domain as the set of all ordered pairs (x,y) such that the denominator is non-zero.

Final Answer

Domain={[(x,y)∈ℝ2,y≠12*x−8]}

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