Show that is strictly monotonic on . Find the domain of the inverse of , denoted by . Find a formula for computing for each in the domain of .
First, to show is strictly increasing on we note that it is strictly increasing on each component (since and are all increasing functions on the domains given). Then we must consider the transition from one of these regions to another. (In other words, we know the function is increasing on each interval, but we need to check that it is increasing from one interval to the next.)
Thus, is indeed increasing on all of .