Find the Domain y=1/2x+3

Problem

y=1/(2*x+3)

Solution

1. Identify the type of function. This is a rational function, which 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 of x

2*x+3=0

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

2*x=−3

4. Divide both sides by 2 to isolate x

x=−3/2

5. State the domain as all real numbers except the value that makes the denominator zero. In interval notation, this excludes −3/2

Final Answer

Domain:(−∞,−3/2)∪(−3/2,∞)

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