Find the Domain y=8/3x-81

Problem

y=8/(3*x−81)

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 of x

3*x−81=0

3. Solve for x by adding 81 to both sides of the equation.

3*x=81

4. Divide both sides by 3 to isolate x

x=27

5. Determine the domain by excluding the value that makes the denominator zero. The domain consists of all real numbers except x=27

Final Answer

Domain: *{x|x∈ℝ,x≠27}

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