Find the Domain y=1/2*(x-4)^2-2

Problem

y=1/2*(x−4)2−2

Solution

1. Identify the type of function. The given equation is a quadratic function in vertex form.

2. Analyze the expression for restrictions. A function's domain is restricted if there are denominators that could equal zero, square roots of negative numbers, or logarithms of non-positive numbers.

3. Determine if any restrictions apply. Since the expression 1/2*(x−4)2−2 involves only subtraction, multiplication, and squaring, it is defined for all real numbers.

4. Conclude the domain. There are no values of x that make the expression undefined.

Final Answer

Domain: *(−∞,∞)

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