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.

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.