Find the Domain 3y=3/2x+6

Problem

3*y=3/(2*x+6)

Solution

1. Isolate the function by dividing both sides of the equation by 3 to express y in terms of x

y=1/(2*x+6)

2. Identify the restriction for a rational function, which is that the denominator cannot be equal to zero.

2*x+6≠0

3. Solve the inequality for x to find the value that must be excluded from the domain.

2*x≠−6

x≠−3

4. State the domain as the set of all real numbers except for the value that makes the denominator zero.

Domain={[x∈ℝ,x≠−3]}

Final Answer

Domain=(−∞,−3)∪(−3,∞)

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