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!