What are inverse functions? Let's start with a definition.
Inverse Function
The inverse of a given function is the interchanging of the domain (independent variable), with the range (dependent variable).
If the original function is f(x), then the inverse function is written as f\(\small\mathsf{ ^{-1} }\)(x).
The superscript of -1 should not be confused with a power.
The inverse does the opposite of a function. For example, if a function says multiply by 3 then add 2, the inverse function does the opposite, which is to subtract 2 and then divide by 3.
Look at the diagram below.
The inverse of this would be:
Question
Suppose you are given the following points for f(x):
{(0, 1), (1, 3), (2, 5), (3, 7)}.
What is the inverse function?
The inverse function interchanges the domain and range. The following points are f\(\small\mathsf{ ^{-1} }\)(x).
{(1, 0), (3, 1), (5, 2), (7, 3)}
{(1, 0), (3, 1), (5, 2), (7, 3)}
