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The question asks for the domain and range of the function \( f(x) = -\log_5(x + 2) \).

### Domain:
- The logarithmic function \( \log_b(x) \) is only defined for \( x > 0 \). For this particular function, \( \log_5(x + 2) \), the argument \( x + 2 \) must be greater than 0.
  - So, \( x + 2 > 0 \) implies \( x > -2 \).
  - Therefore, the domain is \( x > -2 \).

### Range:
- The function \( f(x) = -\log_5(x + 2) \) involves a logarithmic expression. The logarithmic function typically has a range of all real numbers, but since there's a negative sign in front of the logarithm, it reflects the graph across the x-axis.
  - Thus, the range remains all real numbers.

### Conclusion:
The correct answer is:
**A**: Domain: \( x > -2 \), Range: all real numbers.

Would you like a detailed explanation or further clarifications?

Here are 5 related questions for further exploration:
1. How do you determine the domain of any logarithmic function?
2. What happens to the range of a function if it is multiplied by a negative number?
3. How would the domain and range change if the function was \( \log(x - 3) \)?
4. What is the effect of different logarithmic bases on the graph of a logarithmic function?
5. How does a horizontal or vertical shift affect the domain of logarithmic functions?

**Tip**: Remember, the domain of a logarithmic function is always determined by the condition that the argument of the logarithm must be strictly greater than zero.

What are the domain and range of f(x) = -log_5(x + 2)?

Understand how to find the domain and range of the logarithmic function f(x) = -log_5(x + 2). This problem involves logarithmic properties and reflection of graphs, with a step-by-step explanation for students in Grades 9-11.

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