Find the Domain 5- fifth root of x^3-5=-238

Problem

√(5,x^3−5)=−238

Solution

1. Identify the type of function involved in the equation. The expression √(5,x^3−5) is a radical function with an odd index (n=5.

2. Determine the restriction for odd roots. Unlike even roots (like square roots), odd roots are defined for all real numbers, including negative values, zero, and positive values.

3. Analyze the radicand x^3−5 This is a polynomial expression, which is defined for all real numbers x

4. Conclude the domain. Since there are no denominators that could be zero and no even roots, the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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