Let
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.)
and,
Thus, is indeed increasing on all of
.
Next,
When you wrote the inverse function, you got the last part wrong. It should be y^2 / 64.
Thanks! Fixed.