Refresher - Inverse Functions and One-to-One Functions

Refresher

A one to one function is a function in which every element in the range of the function corresponds with one and only one element in the domain. The inverse of a one-to-one function f is denoted by $f^{- 1}$ , where the ordered pairs of $f^{- 1}$ are obtained by interchanging the coordinates in each order pair of $f$ .

Graphically, if a function is one to one, then the function not only passes the vertical line test, but it also passes the horizontal line test.

Horizontal Line Test

If each horizontal line crosses the graph of a function at no more than one point, then the function is one-to-one.

The graph below is the graph of the function $y = - x^{2} + 4$ .
The graph does not pass the horizontal line test.

The graph below is the graph of the function $y = \sqrt (x + 6) - 3$ .
The graph passes the horizontal line test.

Math 1A/1B: Pre-Calculus by Dr. Sarah Eichorn and Dr. Rachel Lehman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Links to an external site..