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Be a continuous function $f: \mathbb{R} \to \mathbb{R}$ such that $f(x)f(f(x)) = 1$ and $f(2020) = 2019$. What is the value of $f(2018)$?

I am having a problem with this question. I already tried, through various attempts, to find the function explicitly which satisfy this condition and $f(0)$ different from $0$. But it leads me to nothing. I am really thinking there is no way to find an explicit function, so I would appreciate any solution to this problem (normally I would prefer a tip, but my ideas are exhausted).

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    $\begingroup$ If this question is from a contest, has the contest expired yet? The question has $2018, 2019, 2020$ so it must have been set recently. $\endgroup$
    – Toby Mak
    Nov 24 '20 at 8:33
  • $\begingroup$ Similar: math.stackexchange.com/q/1464107, math.stackexchange.com/q/2227081 $\endgroup$
    – Martin R
    Nov 24 '20 at 8:46
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    $\begingroup$ It is from a math olympics in 2018. Dont worry @TobyMak, search for "Olimpiadas brasileiras de matematica universitária 2018" $\endgroup$ Nov 24 '20 at 8:47
  • $\begingroup$ Got it, thanks for the information. $\endgroup$
    – Toby Mak
    Nov 24 '20 at 8:48