Find the Domain y=-1/2x^2+4x-2

Problem

y=−1/2*x2+4*x−2

Solution

1. Identify the type of function provided. The expression y=−1/2*x2+4*x−2 is a polynomial function, specifically a quadratic function.

2. Determine if there are any restrictions on the input variable x Restrictions typically occur in cases involving division by zero (rational functions) or taking the square root of a negative number (radical functions).

3. Analyze the expression for such restrictions. Since there are no variables in denominators and no radicals with even indices, the function is defined for all real numbers.

4. Conclude that the domain of any polynomial function is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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