Find the Domain x/(x^3-8)

Problem

x/(x3−8)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

Denominator≠0

2. Set the denominator equal to zero to find the excluded values of x

x3−8=0

3. Solve the equation for x by adding 8 to both sides.

x3=8

4. Take the cube root of both sides to isolate x

x=√(3,8)

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

{x|x∈ℝ,x≠2}

Final Answer

Domain: *(−∞,2)∪(2,∞)

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