Find the Domain g(x) = cube root of x-2

Problem

g(x)=√(3,x−2)

Solution

1. Identify the type of function. The function g(x) is a cube root (an odd root) of a linear expression.

2. Determine the constraints for odd roots. Unlike square roots or other even roots, odd roots are defined for all real numbers, including negative values, zero, and positive values.

3. Analyze the radicand. The expression inside the radical is x−2 which is a polynomial. Polynomials are defined for all real numbers x

4. Conclude the domain. Since there are no values of x that would make the expression undefined (no division by zero and no even roots of negative numbers), the domain is all real numbers.

Final Answer

Domain of *g(x)=(−∞,∞)

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