Find the Domain y=1/3x-6

Problem

y=1/(3*x−6)

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.

3*x−6=0

3. Solve for x by adding 6 to both sides of the equation.

3*x=6

4. Divide both sides by 3 to isolate x

x=2

5. Determine 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|x∈ℝ,x≠2}

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