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

Let’s break this down:

1. Logarithmic and exponential functions are inverses of each other.
2. The domain of the logarithmic function is given as $(-2, \infty)$, meaning the input values (x-values) must be greater than -2.

Since the logarithmic and exponential functions are inverses:

• The domain of the logarithmic function becomes the range of the exponential function.
• Hence, the range of the exponential child function (inverse of the logarithmic function) would be $(-2, \infty)$.

Would you like any further details or explanation on this?

Here are 5 follow-up questions for further understanding:

1. How do logarithmic and exponential functions behave as inverses of each other?
2. What is the general relationship between the domain and range when taking the inverse of a function?
3. Can a logarithmic function have a negative argument? Why or why not?
4. How can you graphically interpret the relationship between a function and its inverse?
5. What are the transformations applied to the standard logarithmic function to get this specific domain?

Tip: When working with inverses of functions, always remember that the domain of one is the range of the other!