MathDB
f(x)+f(1-\frac{1}{x}) = \frac{1}{x}

Source: Mathcenter Contest / Oly - Thai Forum 2011 (R1) p7 sl-9 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 14, 2022
functional equationalgebrafunctional

Problem Statement

Find the function f:R−{0 }→R\displaystyle{f : \mathbb{R}-\left\{ 0\,\right\} \rightarrow \mathbb{R} } such that f(x)+f(1−1x)=1x,   ∀x∈R−{0,1 }f(x)+f(1-\frac{1}{x}) = \frac{1}{x},\,\,\, \forall x \in \mathbb{R}- \{ 0, 1\,\} (-InnoXenT-)
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