Find the Domain y=1/2x-9

Problem

y=1/(2*x−9)

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 value of x

2*x−9=0

3. Solve for x by adding 9 to both sides.

2*x=9

4. Divide both sides by 2 to isolate x

x=9/2

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

Domain={x|x≠9/2}

Final Answer

Domain:(−∞,9/2)∪(9/2,∞)

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