Practice!

Sample Problem

Does the function

  

have an inverse function?

 

Solution

Graph the function to make sure it passes the horizontal line test.

It passes the horizontal line which means it will have an inverse function (which can be easily found by swapping the y and x variables in the two parts of the piecewise function).

In other words, if we were to graph its inverse, the inverse piecewise graph would pass the vertical line test (it’s a function!).