Find the Domain (y^2-16)/(3y+12)

Problem

(y2−16)/(3*y+12)

Solution

1. Identify the condition for the domain of a rational function. A rational function is defined for all real numbers except where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values.

3*y+12=0

3. Solve for y by subtracting 12 from both sides.

3*y=−12

4. Divide both sides by 3 to isolate y

y=−4

5. State the domain as all real numbers except the value that makes the denominator zero.

Final Answer

Domain: *{[y∈ℝ,y≠−4]}

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