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1994 China National Olympiad
3
3
Part of
1994 China National Olympiad
Problems
(1)
China Mathematical Olympiad 1994 problem3
Source: China Mathematical Olympiad 1994 problem3
9/17/2013
Find all functions
f
:
[
1
,
∞
)
→
[
1
,
∞
)
f:[1,\infty )\rightarrow [1,\infty)
f
:
[
1
,
∞
)
→
[
1
,
∞
)
satisfying the following conditions: (1)
f
(
x
)
≤
2
(
x
+
1
)
f(x)\le 2(x+1)
f
(
x
)
≤
2
(
x
+
1
)
; (2)
f
(
x
+
1
)
=
1
x
[
(
f
(
x
)
)
2
−
1
]
f(x+1)=\dfrac{1}{x}[(f(x))^2-1]
f
(
x
+
1
)
=
x
1
[(
f
(
x
)
)
2
−
1
]
.
function
inequalities
algebra unsolved
algebra