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: $(2, \infty)$.

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.