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IMO Longlists
1979 IMO Longlists
21
21
Part of
1979 IMO Longlists
Problems
(1)
All monotonic mappings such that f(t)+f^{-1}(t)=2t
Source: IMO LongList 1979 - P21
6/1/2011
Let
E
E
E
be the set of all bijective mappings from
R
\mathbb R
R
to
R
\mathbb R
R
satisfying
f
(
t
)
+
f
−
1
(
t
)
=
2
t
,
∀
t
∈
R
,
f(t) + f^{-1}(t) = 2t, \qquad \forall t \in \mathbb R,
f
(
t
)
+
f
−
1
(
t
)
=
2
t
,
∀
t
∈
R
,
where
f
−
1
f^{-1}
f
−
1
is the mapping inverse to
f
f
f
. Find all elements of
E
E
E
that are monotonic mappings.
floor function
function
algebra proposed
algebra