Find the Domain y=3 cube root of x

Problem

y=3√(3,x)

Solution

1. Identify the type of function. The given function is a radical function with an index of 3, which is an odd number.

2. Determine the restrictions for odd roots. Unlike square roots or other even roots, the cube root of a number is defined for all real numbers, including negative numbers, zero, and positive numbers.

3. Analyze the expression inside the radical. The radicand is x and there are no denominators or other constraints that would restrict the values x can take.

4. Conclude the domain. Since the cube root is defined for all real values of x the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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