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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.

What is the domain R of the function f(x) = 2 / (x + 2)?

Learn how to find the domain of the rational function f(x) = 2 / (x + 2). This problem involves identifying restrictions in the denominator, such as when the denominator equals zero. Suitable for students in Grades 9-12.

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