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).
