Find the Domain cube root of 2x^2-8

Problem

√(3,2*x2−8)

Solution

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

2. Determine the constraints for odd roots. Unlike square roots (even roots), which require the radicand to be non-negative, cube roots are defined for all real numbers.

3. Analyze the radicand 2*x2−8 This is a polynomial expression, which is defined for all real values of x

4. Conclude that since there are no values of x that make the expression undefined, the domain consists of all real numbers.

Final Answer

Domain of √(3,2*x2−8)=(−∞,∞)

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