# From An Erroneous Problem

Algebra Level 2

Function $$f: \mathbb {R \to R}$$ satisfies

$\large f(x) + f \left(1-\frac 1x\right) = 1+x$

for $$x \ne 0$$ and $$x \ne 1$$. Then $$2017 - 2f(2017) = \dfrac 1{k(k-1)}$$, where $$k$$ is a positive integer. Find $$k$$.

A corrected problem from Priyanshu Mishra.

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