Find the Domain cube root of 729x^3

Problem

√(3,729*x3)

Solution

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

2. Determine the constraints for odd roots. Unlike square roots, the radicand (the expression inside the root) of a cube root can be any real number, including negative values, zero, and positive values.

3. Analyze the radicand 729*x3 Since 729*x3 is a polynomial, it is defined for all real values of x

4. Conclude the domain. Because there are no restrictions such as division by zero or even roots of negative numbers, the domain is the set of all real numbers.

Final Answer

Domain of √(3,729*x3)=(−∞,∞)

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