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P23 [Algebra] - Turkish NMO 1st Round - 2013

Source:

April 20, 2013
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Problem Statement

If the conditions f(2x+1)+g(3−x)=xf((3x+5)/(x+1))+2g((2x+1)/(x+1))=x/(x+1)\begin{array}{rcl} f(2x+1)+g(3-x) &=& x \\ f((3x+5)/(x+1))+2g((2x+1)/(x+1)) &=& x/(x+1) \end{array} hold for all real numbers x≠1x\neq 1, what is f(2013)f(2013)?
<spanclass=′latex−bold′>(A)</span> 1007<spanclass=′latex−bold′>(B)</span> 40213<spanclass=′latex−bold′>(C)</span> 60377<spanclass=′latex−bold′>(D)</span> 40295<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 1007 \qquad<span class='latex-bold'>(B)</span>\ \dfrac {4021}{3} \qquad<span class='latex-bold'>(C)</span>\ \dfrac {6037}7 \qquad<span class='latex-bold'>(D)</span>\ \dfrac {4029}{5} \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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