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The problem asks about the range of an exponential function, which is the inverse of a logarithmic function with a given domain.

### Key Information:
- The domain of the logarithmic function is \((-2, \infty)\).
- The exponential function is the inverse of the logarithmic function.
- The domain of the logarithmic function becomes the range of its inverse (exponential) function.

### Explanation:
The domain of a logarithmic function becomes the range of its inverse, the exponential function, and vice versa. Therefore, since the logarithmic function has a domain of \((-2, \infty)\), this will also be the range of the inverse exponential function.

Thus, the range of the exponential function is:
\[
\boxed{(2, \infty)}
\]

The correct answer is **B**: \((2, \infty)\).

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Would you like further clarification? Here are five related questions to expand on this topic:

1. What is the relationship between the domain and range of inverse functions in general?
2. How do you find the inverse of a logarithmic function algebraically?
3. What are some transformations that can shift the domain of a logarithmic function?
4. How does the base of a logarithmic function affect its inverse?
5. Can the domain of a logarithmic function include negative numbers, and why?

**Tip:** When dealing with logarithmic functions, always check the domain carefully since logs are only defined for positive inputs.

A logarithmic child function has domain of (-2, ∞). What is the range of the exponential child function that is its inverse?

Understand how to find the range of an exponential function, the inverse of a logarithmic function with a domain of (-2, ∞). Learn the core concepts of logarithmic and exponential functions and their inverses. Suitable for students in Grades 10-12.

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