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National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2018 Turkey Team Selection Test
2
2
Part of
2018 Turkey Team Selection Test
Problems
(1)
Functional Equation
Source: Turkey Team Selection Test 2018 P2
3/26/2018
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
.
functional equation
TST
Turkey
2018