## Problem of the Day #253: A Game of Lexes
*November 27, 2011*

*Posted by Saketh in : potd , trackback*

Alex, Elex, Ilex, and Olex are playing a game with some function $f(x)$. First, Alex selects a real number $x$. Elex then finds the value of $f(x)$, and Ilex computes the value of $f(\frac{1}{1-x})$. Finally, Olex calls out the sum of Elex’s and Ilex’s numbers.

Ulex observes that for any value of $x$ other than $0$ and $1$, Olex will simply state the initial value of $x$. Given this information, find $f(2011)$.

**Bonus:** Find a closed form expression for $f(x)$.

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