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Turkey Team Selection Test
2018 Turkey Team Selection Test
2
Functional Equation
Functional Equation
Source: Turkey Team Selection Test 2018 P2
March 26, 2018
functional equation
TST
Turkey
2018
Problem Statement
Find all
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
surjective functions such that
f
(
x
f
(
y
)
+
y
2
)
=
f
(
(
x
+
y
)
2
)
−
x
f
(
x
)
f(xf(y)+y^2)=f((x+y)^2)-xf(x)
f
(
x
f
(
y
)
+
y
2
)
=
f
((
x
+
y
)
2
)
−
x
f
(
x
)
for all real numbers
x
,
y
x,y
x
,
y
.
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