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Iran Team Selection Test
2007 Iran Team Selection Test
3
A routine Functional Equation
A routine Functional Equation
Source: Iran TST 2007, Day 1
May 5, 2007
algebra proposed
algebra
Problem Statement
Find all solutions of the following functional equation:
f
(
x
2
+
y
+
f
(
y
)
)
=
2
y
+
f
(
x
)
2
.
f(x^{2}+y+f(y))=2y+f(x)^{2}.
f
(
x
2
+
y
+
f
(
y
))
=
2
y
+
f
(
x
)
2
.
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