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Kosovo Mathematical Olympiad 2016 TST , Problem 4
Kosovo Mathematical Olympiad 2016 TST , Problem 4
Source:
January 9, 2017
functional equation
Problem Statement
It is given the function
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
fow which
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and for all
x
∈
R
x\in\mathbb{R}
x
∈
R
satisfied
f
(
x
+
5
)
≥
f
(
x
)
+
5
f(x+5)\geq f(x)+5
f
(
x
+
5
)
≥
f
(
x
)
+
5
and
f
(
x
+
1
)
≤
f
(
x
)
+
1
f(x+1)\leq f(x)+1
f
(
x
+
1
)
≤
f
(
x
)
+
1
If
g
(
x
)
=
f
(
x
)
−
x
+
1
g(x)=f(x)-x+1
g
(
x
)
=
f
(
x
)
−
x
+
1
then find
g
(
2016
)
g(2016)
g
(
2016
)
.
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