AoPS Wiki talk:Problem of the Day/June 9, 2011
Problem
AoPSWiki:Problem of the Day/June 9, 2011
Solution
Let . Therefore,
. Now, let
be the inverse function of
, so that
. However, the
in the LHS cancels out by the definition of an inverse function. Therefore, we have
. Now we must find
. Again by the definition of an inverse function, we have
, and
, so
. Solving, we find that
. Plugging this in to
yields
.