MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2015 India National Olympiad
3
3
Part of
2015 India National Olympiad
Problems
(1)
INMO 2015
Source: inmo 2015 #3
2/1/2015
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
)
.
function
trigonometry
algebra
functional equation
algebra unsolved