We are asked to find the domain of the function $f(x) = \frac{2}{x+2}$.

To find the domain of this rational function, we need to identify where the denominator is equal to zero, as division by zero is undefined.

1. Set the denominator $x + 2 = 0$.
2. Solving for $x$, we get $x = -2$.

Thus, the function is undefined at $x = -2$. Therefore, the domain of the function is all real numbers except $x = -2$.

This can be written as the union of two intervals: $D = (-\infty, -2) \cup (-2, +\infty)$

The correct answer is D) $D = (-\infty, -2) \cup (-2, +\infty)$.

Let me know if you'd like further explanation or have any questions!

Here are five related questions you might want to consider:

1. How do you determine the domain of a function with multiple restrictions (e.g., square roots and fractions)?
2. What is the domain of the function $f(x) = \frac{1}{x^2 - 4}$?
3. How do you find the range of a rational function?
4. What happens to the graph of a rational function at points where the function is undefined?
5. Can the domain of a function include infinity?

Tip: When determining the domain of a rational function, always check where the denominator becomes zero. These are the points where the function is undefined.