Find the Domain y=1/2x+4

Problem

y=1/(2*x+4)

Solution

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

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

2*x+4=0

3. Solve for x by subtracting 4 from both sides.

2*x=−4

4. Divide both sides by 2 to isolate x

x=−2

5. State the domain by excluding the value that makes the denominator zero. The domain consists of all real numbers except x=−2

Final Answer

Domain: *{[x∈ℝ,x≠−2]}

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