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Pan African
2008 Pan African
1
f(x+y) is at most f(x)+f(y), which is at most x+y
f(x+y) is at most f(x)+f(y), which is at most x+y
Source: Pan African Olympiad 2008
October 1, 2011
function
algebra proposed
algebra
Problem Statement
Determine all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
satisfying
f
(
x
+
y
)
≤
f
(
x
)
+
f
(
y
)
≤
x
+
y
f(x+y)\le f(x)+f(y)\le x+y
f
(
x
+
y
)
≤
f
(
x
)
+
f
(
y
)
≤
x
+
y
for all
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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