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2012 Cuba MO
7
f(x^2 + f(y)) = y - x^2
f(x^2 + f(y)) = y - x^2
Source: 2012 Cuba MO 2.7
September 18, 2024
algebra
functional
functional equation
Problem Statement
Find all the functions
f
:
R
→
R
f : R\to R
f
:
R
→
R
such that
f
(
x
2
+
f
(
y
)
)
=
y
−
x
2
f(x^2 + f(y)) = y - x^2
f
(
x
2
+
f
(
y
))
=
y
−
x
2
for all
x
,
y
x, y
x
,
y
reals.
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