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National and Regional Contests
Greece Contests
Greece National Olympiad
1997 Greece National Olympiad
2
2
Part of
1997 Greece National Olympiad
Problems
(1)
Find f(1)
Source: Greek national M.O. 1997, Final Round, problem 2
11/20/2011
Let a function
f
:
R
+
→
R
f : \Bbb{R}^+ \to \Bbb{R}
f
:
R
+
→
R
satisfy: (i)
f
f
f
is strictly increasing, (ii)
f
(
x
)
>
−
1
/
x
f(x) > -1/x
f
(
x
)
>
−
1/
x
for all
x
>
0
x > 0
x
>
0
, (iii)
f
(
x
)
f
(
f
(
x
)
+
1
/
x
)
=
1
f(x)f (f(x) + 1/x) = 1
f
(
x
)
f
(
f
(
x
)
+
1/
x
)
=
1
for all
x
>
0
x > 0
x
>
0
. Determine
f
(
1
)
f(1)
f
(
1
)
.
function
algebra unsolved
algebra