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
.
Another solution:
We know that f(x) is of the form ax+b, so we can start by plugging in x=1 which yields f(1)=7 and plugging in x=-1 gives f(0)=3, using the slope formula we can get f(x)=4x+3