Find the Domain 9x^3+2x-8x^3-3x

Problem

9*x3+2*x−8*x3−3*x

Solution

1. Identify the type of function represented by the expression. The expression 9*x3+2*x−8*x3−3*x is a polynomial.

2. Recall the definition of the domain for polynomial functions. A polynomial is defined for all real numbers because there are no denominators that could be zero and no even-indexed roots of negative numbers.

3. Simplify the expression by combining like terms to confirm it remains a polynomial.

9*x3−8*x3+2*x−3*x

x3−x

4. Determine the domain based on the properties of polynomials. Since x3−x is defined for every real value of x the domain is all real numbers.

Final Answer

Domain: *(−∞,∞)

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