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2018 Brazil Undergrad MO
13
13
Part of
2018 Brazil Undergrad MO
Problems
(1)
Calculate the value of f (2018)
Source: Brazil Undergrad MO - Galois-Noether 2018 #13
11/26/2019
A continuous function
f
:
R
ā
R
f: \mathbb {R} \to \mathbb {R}
f
:
R
ā
R
satisfies
f
(
x
)
f
(
f
(
x
)
)
=
1
f (x) f (f (x)) = 1
f
(
x
)
f
(
f
(
x
))
=
1
for every real
x
x
x
and
f
(
2020
)
=
2019
f (2020) = 2019
f
(
2020
)
=
2019
. What is the value of
f
(
2018
)
f (2018)
f
(
2018
)
?
function
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