Find the Domain (x-5)^2+3(x-1)^2-(8x+1)^2

Problem

(x−5)2+3*(x−1)2−(8*x+1)2

Solution

1. Identify the type of expression provided. The expression (x−5)2+3*(x−1)2−(8*x+1)2 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. Determine the set of all possible input values for x Since there are no restrictions on the variable x in a polynomial expression, the domain is all real numbers.

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

Final Answer

Domain: *(−∞,∞)

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