https://file.aiquickdraw.com/mathbot/file/1726766664796b8r51ks4.jpg

The statement in the image says, "The domain of a function is the range of its inverse."

This is **True**. 

Explanation:
For a function \( f(x) \) and its inverse \( f^{-1}(x) \), the following relationships hold:
- The domain of \( f(x) \) is the set of all possible input values for \( f(x) \).
- The range of \( f(x) \) is the set of all possible output values for \( f(x) \).

When we reverse the process for the inverse function:
- The domain of \( f^{-1}(x) \) is the range of \( f(x) \), and
- The range of \( f^{-1}(x) \) is the domain of \( f(x) \).

So, the domain of the function is indeed the range of its inverse. Hence, the correct answer is **A. True**.

Would you like further details or have any questions?

Here are five related questions to expand on this:

1. What are the conditions for a function to have an inverse?
2. How does the horizontal line test help determine if a function has an inverse?
3. Can all functions have inverses? Why or why not?
4. What is the graphical relationship between a function and its inverse?
5. How does the domain and range of composite functions relate to their inverses?

**Tip**: If a function passes the horizontal line test, it is one-to-one and has an inverse!

The domain of a function is the range of its inverse.

Explore how the domain of a function relates to the range of its inverse with a step-by-step explanation. Suitable for students in Grades 9-12 learning about inverse 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