Find the Domain f(x)=(x-3)(x-2i)(x+2i)

Problem

ƒ(x)=(x−3)*(x−2*i)*(x+2*i)

Solution

1. Identify the type of function provided. The expression ƒ(x)=(x−3)*(x−2*i)*(x+2*i) is a polynomial function.

2. Expand the expression to verify its form. Multiplying the conjugate factors (x−2*i)*(x+2*i) results in x2+4

3. Simplify the full expression. Multiplying (x−3)*(x2+4) results in x3−3*x2+4*x−12

4. Determine the domain. Since ƒ(x) is a polynomial, it is defined for all real numbers unless otherwise specified. There are no denominators, square roots of negative variables, or logarithms to restrict the input.

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

Final Answer

Domain:(−∞,∞)

Want more problems? Check here!