MathDB
Problems
Contests
Undergraduate contests
Brazil Undergrad MO
2019 Brazil Undergrad MO
4
Normal function.
Normal function.
Source:
November 16, 2019
algebra
function
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
ā
R
such that for any
(
x
,
y
)
(x, y)
(
x
,
y
)
real numbers we have
f
(
x
f
(
y
)
+
f
(
x
)
)
+
f
(
y
2
)
=
f
(
x
)
+
y
f
(
x
+
y
)
f(xf(y)+f(x))+f(y^2)=f(x)+yf(x+y)
f
(
x
f
(
y
)
+
f
(
x
))
+
f
(
y
2
)
=
f
(
x
)
+
y
f
(
x
+
y
)
Back to Problems
View on AoPS