MathDB
Problems
Contests
Undergraduate contests
Brazil Undergrad MO
2016 Brazil Undergrad MO
2
2
Part of
2016 Brazil Undergrad MO
Problems
(1)
YAFTFP - Yet Another "Find The Functions" Problem
Source: 38th Brazilian Undergrad MO (2016) - First Day, Problem 2
11/25/2016
Find all functions
f
:
R
→
R
f:\mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
2
+
y
2
f
(
x
)
)
=
x
f
(
y
)
2
−
f
(
x
)
2
f(x^2+y^2f(x)) = xf(y)^2-f(x)^2
f
(
x
2
+
y
2
f
(
x
))
=
x
f
(
y
)
2
−
f
(
x
)
2
for every
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
functional equation