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Korea Junior Mathematics Olympiad
2015 Korea Junior Math Olympiad
6
Injective Function, FE
Injective Function, FE
Source: 2015 Korean Junior MO P6
November 1, 2015
function
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that (i): For different reals
x
,
y
x,y
x
,
y
,
f
(
x
)
≠
f
(
y
)
f(x) \not= f(y)
f
(
x
)
=
f
(
y
)
.(ii): For all reals
x
,
y
x,y
x
,
y
,
f
(
x
+
f
(
f
(
−
y
)
)
)
=
f
(
x
)
+
f
(
f
(
y
)
)
f(x+f(f(-y)))=f(x)+f(f(y))
f
(
x
+
f
(
f
(
−
y
)))
=
f
(
x
)
+
f
(
f
(
y
))
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