Define functions and
as follows:
Find a formula for and find the values at which
is continuous.
If then
and so
. Therefore, by the definition of
,
If , then
and so again
Next, if then
and so
Finally, if , then
and we have
Putting this all together we have
From this expression we have is continuous everywhere except at
and
.
a bit of a detail but in the end it’s
,
.
Thanks! Fixed!