# Find a function satisfying this condition [duplicate]

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).

• 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. Nov 24 '20 at 8:33
• Nov 24 '20 at 8:46
• It is from a math olympics in 2018. Dont worry @TobyMak, search for "Olimpiadas brasileiras de matematica universitária 2018" Nov 24 '20 at 8:47
• Got it, thanks for the information. Nov 24 '20 at 8:48