Find the Domain 1/81x^6-8/27x^3+16/9

Problem

ƒ(x)=1/81*x6−8/27*x3+16/9

Solution

1. Identify the type of function. The expression is a polynomial of degree 6.

2. Recall the definition of a domain for polynomial functions. Polynomials are defined for all real numbers because they do not involve division by variables, square roots of negative numbers, or logarithms of non-positive numbers.

3. Determine the set of all possible input values for x Since there are no restrictions on the variable x the domain consists of all real numbers.

4. Express the domain in interval notation. The set of all real numbers is represented as (−∞,∞)

Final Answer

Domain: *(−∞,∞)

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