Find the Domain 3x+12y=2

Problem

3*x+12*y=2

Solution

1. Identify the type of equation. The given equation 3*x+12*y=2 is a linear equation in two variables.

2. Solve for y in terms of x to express the relation as a function.

12*y=−3*x+2

3. Divide by 12 to isolate y

y=−3/12*x+2/12

4. Simplify the fractions.

y=−1/4*x+1/6

5. Analyze the resulting function. Since y=−1/4*x+1/6 is a polynomial (specifically a linear function), there are no values of x that result in division by zero or the square root of a negative number.

6. Determine the domain. The function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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