Find the Domain and Range y = cube root of x

Problem

y=√(3,x)

Solution

1. Identify the type of function. The function y=√(3,x) is a cube root function, which is an odd root.

2. Determine the domain. Unlike square roots, cube roots are defined for all real numbers because the cube of a negative number is negative, the cube of zero is zero, and the cube of a positive number is positive.

3. State the domain in interval notation. Since x can be any real value, the domain is (−∞,∞)

4. Determine the range. As x approaches infinity, √(3,x) approaches infinity. As x approaches negative infinity, √(3,x) approaches negative infinity.

5. State the range in interval notation. Since y can take on any real value, the range is (−∞,∞)

Final Answer

Domain: *(−∞,∞), Range: *(−∞,∞)

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