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2012 Turkey MO (2nd round)
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2012 Turkey MO (2nd round)
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(1)
Turkey NMO 2012 Problem 3 functional equation
Source: Turkey NMO 2012
11/24/2012
Find all non-decreasing functions from real numbers to itself such that for all real numbers
x
,
y
x,y
x
,
y
f
(
f
(
x
2
)
+
y
+
f
(
y
)
)
=
x
2
+
2
f
(
y
)
f(f(x^2)+y+f(y))=x^2+2f(y)
f
(
f
(
x
2
)
+
y
+
f
(
y
))
=
x
2
+
2
f
(
y
)
holds.
function
algebra
functional equation
algebra proposed