AoPS Wiki talk:Problem of the Day/June 9, 2011
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[hide]Problem
AoPSWiki:Problem of the Day/June 9, 2011
Solution
Solution 1
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 .
Solution 2
We know that is of the form , so we can start by plugging in which yields and plugging in gives , using the slope formula we can get