Final answer:
The domain of the function √(2x + 16) is all x values that keep the radicand non-negative. The radicand 2x + 16 must be greater than or equal to 0, which gives a domain of [-8, ∞) in interval notation.
Step-by-step explanation:
Finding the Domain of a Square Root Function
To find the domain of the square root function √(2x + 16), it is important to recognize that the expression inside the square root, known as the radicand, must be greater than or equal to zero. This is because the square root of a negative number is not defined in the set of real numbers, which is typically the context for high school mathematics. Therefore, the domain of the function is all x values that make the radicand non-negative.
To find the domain, set up an inequality with the radicand:
2x + 16 ≥ 0. Solving this inequality for x gives x ≥ -8. Thus, the domain of the function in interval notation is [-8, ∞).
This process does not involve complex operations such as completing the square or solving quadratic equations. Instead, the focus is on ensuring that the radicand of the square root is non-negative.
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