Answer
There is a one-to-one correspondence between the time of the day and the average level of happiness on the intervals $[8,8.5]$, $[19,20]$, and $[21,22]$. During the rest of the time, there is no inverse function because the graph does not pass the horizontal line test.
Work Step by Step
When we draw a horizontal line, we realize that the graph as a whole is not one-to-one and therefore lacks an inverse.
