Hello!
You wrote
By the definition of an inverse function of
is that number
for which
Usually we require that such a number must be unique, otherwise
would be a many-valued function.
a. In other words, we need to solve the equation
In our problem, takes any value infinitely many times, even at the given interval
even at any neighborhood of
The cause of this is that tends to
at points where
for some integer
The
part remains finite and bounded at any finite interval and cannot prevent this behavior of
These points are
and they tend to zero as
tends to
Regardless of the number of solutions, the equation which is equivalent to
cannot be solved exactly.
I might suppose that you misprint the formula, probably In that case, the only solution for
at the interval
is
This is because
is strictly monotone on
It is not obvious but true. Ask me if you need a proof.
b. If exists, then by definition
No comments:
Post a Comment