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National and Regional Contests
Spain Contests
pOMA and PErA mathematical olympiads
2024 PErA
P5
P5
Part of
2024 PErA
Problems
(1)
Clean R+ to R+ FE
Source: PErA 2024/5
3/4/2024
Find all functions
f
:
R
+
→
R
+
f\colon \mathbb{R}^+ \to \mathbb{R}^+
f
:
R
+
→
R
+
such that
f
(
x
f
(
x
)
+
y
2
)
=
x
2
+
y
f
(
y
)
f(xf(x)+y^2) = x^2+yf(y)
f
(
x
f
(
x
)
+
y
2
)
=
x
2
+
y
f
(
y
)
for any positive reals
x
,
y
x,y
x
,
y
.
functional equation
function
algebra