Determine the Domain of the Function: Analyzing (2x+2)/√(x-16)

To determine the domain of the function $\frac{2x+2}{\sqrt{x-16}}$, follow these steps:

• Step 1: Identify the constraint imposed by the square root in the denominator.
• Step 2: Solve the inequality $x-16 > 0$.
• Step 3: Interpret the solution in terms of the domain.

Let's proceed:

Step 1: The function $\frac{2x+2}{\sqrt{x-16}}$ has a square root in the denominator. For the square root to be defined in the real number system and prevent division by zero, the expression under the square root, $x-16$, must be greater than zero.

Step 2: Solve the inequality:

$x - 16 > 0$

Add 16 to both sides:

$x > 16$

Step 3: The solution $x > 16$ means that the domain of the function is all real numbers greater than 16.

Therefore, the domain of the function is $x > 16$, which corresponds to choice 2.