Question

Matching
2 points
RULE: To find an ordered pair of a function's inverse, switch the x- and y-coordinates.
Inverse
Function
(y, x)
(x, y)

Answer 1

To find the inverse of a function, you indeed switch the x- and y-coordinates to create ordered pairs. To help illustrate this, here is how you would typically do this:

Given a function in the form \( f(x) = y \), the inverse function, denoted as \( f^{-1}(x) \), can be obtained by following these steps:

1. **Express the output as an ordered pair**: For each input \( x \), find the corresponding output \( y \). This gives you pairs such as \( (x, y) \).

2. **Switch the coordinates**: Once you have the ordered pair \( (x, y) \), switch them to \( (y, x) \).

As an example:

- Assume a function \( f \) gives the ordered pairs:
- \( (1, 2) \)
- \( (3, 4) \)

- The ordered pairs of the inverse function \( f^{-1} \) would be:
- \( (2, 1) \)
- \( (4, 3) \)

So whenever you're given a list of ordered pairs of a function, simply switch each pair to find the corresponding pairs for the inverse function.

If you have specific pairs you'd like to match or are looking for, please provide them, and I can assist you further!