Consider the function: Now, interchange the x- and y- coordinates in the set of ordered pairs above. This new set of ordered pairs is called the inverse of the function f (x). Denote by f -1 (x). What is the algebraic view of f -1 (x)?

Example:

Examine these tables.

Example 1:

Example 2:

Is the inverse of a function another function? NO!! Examine the graphs below.

Since the function fails the “Horizontal Line Test”, the inverse is not a function. Horizontal Line Test Since the function passes the “Horizontal Line Test”, the inverse is a function.

Example 3:

Example 4:

In Summary

Examples