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National and Regional Contests
India Contests
India National Olympiad
2015 India National Olympiad
3
INMO 2015
INMO 2015
Source: inmo 2015 #3
February 1, 2015
function
trigonometry
algebra
functional equation
algebra unsolved
Problem Statement
Find all real functions
f
:
R
ā
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
such that
f
(
x
2
+
y
f
(
x
)
)
=
x
f
(
x
+
y
)
f(x^2+yf(x))=xf(x+y)
f
(
x
2
+
y
f
(
x
))
=
x
f
(
x
+
y
)
.
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