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

A.(-2, ∞)

B.(2, ∞)

C.(-∞, -2)

D.(-∞, 2)

To solve this, we need to recognize that the logarithmic function and the exponential function are inverses of each other. 

Given the domain of the logarithmic function is \((-2, \infty)\), we know that the range of the exponential function (its inverse) will be the same as the domain of the logarithmic function, but in the context of an inverse, we must switch the domain and range between the two.

Thus, the range of the exponential function, which is the inverse, will be \((-2, \infty)\).

### Answer: 
**A. (-2, ∞)**

Would you like further details or have any questions?

Here are 5 related questions to expand on the topic:
1. What is the general relationship between a function and its inverse in terms of domain and range?
2. How do we derive the inverse of a logarithmic function?
3. What are the key properties of logarithmic functions that affect their inverses?
4. How does the base of a logarithmic or exponential function affect the domain and range?
5. Can a logarithmic function have a negative domain?

**Tip:** Remember, for any function \( f(x) \) and its inverse \( f^{-1}(x) \), the domain of \( f(x) \) becomes the range of \( f^{-1}(x) \), and vice versa.

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

A. (-2, ∞)
B. (2, ∞)
C. (-∞, -2)
D. (-∞, 2)

Explore how to find the range of the exponential function that is the inverse of a logarithmic function with a domain of (-2, ∞). This math problem covers key concepts in logarithmic and exponential functions, focusing on the inverse relationship. Suitable for high school students in Grades 10-12.

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