Find the Domain f(x)-10000+400x-2x^2

Problem

ƒ(x)=−10000+400*x−2*x2

Solution

1. Identify the type of function. The expression ƒ(x)=−2*x2+400*x−10000 is a polynomial function, specifically a quadratic.

2. Check for restrictions. Polynomial functions do not contain any operations that restrict the input, such as division by zero (fractions) or taking the square root of a negative number (even roots).

3. Determine the set of all possible input values. Since any real number can be squared, multiplied, and added, the function is defined for 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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