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The question asks for the inverse of the function \( f = \{(1, 1), (2, 2), (3, 3), (4, 4)\} \).

To find the inverse of a function, you swap the elements in each ordered pair. For example, if the function includes \( (a, b) \), then its inverse will include \( (b, a) \).

Let's look at the function:

- \( (1, 1) \) becomes \( (1, 1) \)
- \( (2, 2) \) becomes \( (2, 2) \)
- \( (3, 3) \) becomes \( (3, 3) \)
- \( (4, 4) \) becomes \( (4, 4) \)

Since all pairs are of the form \( (x, x) \), the inverse is exactly the same as the original function.

Thus, the correct answer is:

- **\( \{(1, 1), (2, 2), (3, 3), (4, 4)\} \)**.

Let me know if you'd like further clarification or have any questions.

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Here are five related questions:
1. What is the general process for finding the inverse of a function?
2. How does one confirm whether a function is its own inverse?
3. Are all functions invertible? Why or why not?
4. What is the difference between one-to-one and onto functions regarding inverses?
5. Can a function have more than one inverse?

**Tip:** A function will only have an inverse if it is a one-to-one (injective) function.

Which of the following is the inverse of \( \{(1, 1), (2, 2), (3, 3), (4, 4)\} \)?

Learn how to find the inverse of a function represented by ordered pairs like \( \{(1, 1), (2, 2), (3, 3), (4, 4)\} \). This problem is ideal for students in Grades 9-10 and covers key concepts in inverse functions.

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