Find the Domain 15(1/3x-8)

Problem

15*(1/(3*x−8))

Solution

1. Identify the type of function. The expression is a rational function because it contains a variable in the denominator.

2. Determine the restriction for the domain. For a rational expression to be defined, the denominator must not equal zero.

3. Set up the inequality to find the excluded value of x

3*x−8≠0

4. Solve for x by adding 8 to both sides.

3*x≠8

5. Divide both sides by 3 to isolate x

x≠8/3

6. Express the domain in interval notation. The domain includes all real numbers except 8/3

Final Answer

Domain: *(−∞,8/3)∪(8/3,∞)

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