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TR-MO-R1 2015 Problem 15

    f:R→Rf : \mathbf{R} \to \mathbf{R} ve g:R→Rg : \mathbf{R} \to \mathbf{R} fonksiyonları, her x≠0x \neq 0 için

    f(2x+1)+g(x−1)=3x+2f(2x+1) + g(x-1) = 3x + 2

    f(x+1x)+3g(1−2x2x)=12x+4f\left(\frac{x+1}{x}\right) + 3g\left(\frac{1-2x}{2x}\right) = \frac{1}{2x} + 4

    eşitliklerini sağlıyorsa f(2015)+g(2015)f(2015) + g(2015) kaçtır?

    a) −2016-2016 b) −2015-2015 c) 20142014 d) 20152015 e) Hiçbiri

    Official text Turkish Mathematical Olympiad, first round 2015 official paper, page 5. Quoted with source.

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