Find the Domain fifth root of -32(x-2)^5

Problem

√(5,−32*(x−2)5)

Solution

1. Identify the type of function. The expression is a fifth root, which is an odd root.

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

3. Analyze the radicand. The expression inside the root, −32*(x−2)5 is a polynomial.

4. Conclude that since polynomials are defined for all real numbers and odd roots have no domain restrictions, the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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