Find the Domain f(x)=2x(x-4)+7

Problem

ƒ(x)=2*x*(x−4)+7

Solution

1. Identify the type of function provided. The expression ƒ(x)=2*x*(x−4)+7 is a polynomial function.

2. Expand the expression to confirm its form. Multiplying 2*x by (x−4) gives 2*x2−8*x so the function is ƒ(x)=2*x2−8*x+7

3. Determine if there are any restrictions. Polynomials do not have denominators that could be zero or square roots of negative numbers.

4. Conclude that the function is defined for all real numbers.

Final Answer

Domain: *(−∞,∞)

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