Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 1 / e / i

Replace $x$ by $1/x$, which stays in the domain of the functional equation. Writing $u=f(x)$ and $v=f(1/x)$ gives the linear systemTwice the second equation minus the first gives $3u=2/x-x$, so the only possible function isTo check existence as well as uniqueness, substitute this expression: $f(x)+2f(1/x)=(2/x-x+4x-2/x)/3=x$.