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Thailand Contests
Thailand National Olympiad
2019 Thailand Mathematical Olympiad
3
3
Part of
2019 Thailand Mathematical Olympiad
Problems
(1)
FE on positive reals with a surprise
Source: 2019 Thailand Mathematical Olympiad P3
5/22/2019
Find all functions
f
:
R
+
→
R
+
f:\mathbb{R}^+\to\mathbb{R}^+
f
:
R
+
→
R
+
such that
f
(
x
+
y
f
(
x
)
+
y
2
)
=
f
(
x
)
+
2
y
f(x+yf(x)+y^2) = f(x)+2y
f
(
x
+
y
f
(
x
)
+
y
2
)
=
f
(
x
)
+
2
y
for every
x
,
y
∈
R
+
x,y\in\mathbb{R}^+
x
,
y
∈
R
+
.
algebra