We are given the function $f(x) = \{(1, 2), (3, 4), (5, 6), (7, 8)\}$. To find the domain of the inverse function $f^{-1}(x)$, let's follow these steps:

Key Concepts:

• The domain of a function consists of the input values (x-values).
• The range of a function consists of the output values (y-values).
• For the inverse function $f^{-1}(x)$, the domain and range are swapped. This means that the range of $f(x)$ will become the domain of $f^{-1}(x)$.

Solution:

For the given function $f(x) = \{(1, 2), (3, 4), (5, 6), (7, 8)\}$:

• The domain of $f(x)$ is {1, 3, 5, 7} (the x-values).
• The range of $f(x)$ is {2, 4, 6, 8} (the y-values).

Therefore, the domain of the inverse function $f^{-1}(x)$ is the range of the original function $f(x)$, which is {2, 4, 6, 8}.

Answer:

The correct choice is B. 2, 4, 6, and 8.

Do you want any further details or explanations?

Here are 5 related questions you might find helpful:

1. What is the range of the inverse function $f^{-1}(x)$?
2. How do you determine if a function has an inverse?
3. What happens to the graph of a function and its inverse?
4. Can all functions have inverses? Why or why not?
5. What are common properties of inverse functions?

Tip: When solving for the inverse function, always swap the x- and y-values from the original function's domain and range.