https://file.aiquickdraw.com/mathbot/file/1726769492938bbj96lms.jpg

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!

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

Explore the relationship between logarithmic and exponential functions. Given a logarithmic function with domain (-2, ∞), discover how the domain of one function corresponds to the range of its inverse. Suitable for high school students studying algebra and advanced functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation