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

Problem

ƒ(x)=(x+3)2−3

Solution

1. Identify the type of function. The expression ƒ(x)=(x+3)2−3 is a polynomial function, specifically a quadratic function in vertex form.

2. Analyze the constraints for the domain. For a function to have a restricted domain, there must be operations that are undefined for certain real numbers, such as division by zero or taking the square root of a negative number.

3. Determine if any restrictions exist. Since the function only involves addition, subtraction, and squaring, it is defined for all real numbers x

4. State the domain in interval notation. Because there are no restrictions, the domain includes every value from negative infinity to positive infinity.

Final Answer

Domain:(−∞,∞)

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