Find the Domain cube root of n+3* cube root of n^2-3n+9

Problem

√(3,n+3)⋅√(3,n2−3*n+9)

Solution

1. Identify the type of function involved in the expression. The expression consists of the product of two cube root functions.

2. Determine the domain of a cube root function. For any expression √(3,ƒ(n)) the cube root is defined for all real numbers because the index is odd.

3. Analyze the radicands. The expressions n+3 and n2−3*n+9 are polynomials, which are defined for all real numbers n

4. Conclude that since there are no even roots, denominators, or logarithms to restrict the input, the domain is the set of all real numbers.

Final Answer

Domain=(−∞,∞)

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