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2018-IMOC
A4
A4
Part of
2018-IMOC
Problems
(1)
f(x^2+f(y))-y=(f(x+y)-y)^2 over R
Source: IMOC 2018 A4
8/15/2021
Find all functions
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
such that
f
(
x
2
+
f
(
y
)
)
−
y
=
(
f
(
x
+
y
)
−
y
)
2
f\left(x^2+f(y)\right)-y=(f(x+y)-y)^2
f
(
x
2
+
f
(
y
)
)
−
y
=
(
f
(
x
+
y
)
−
y
)
2
holds for all
x
,
y
∈
R
x,y\in\mathbb R
x
,
y
∈
R
.
fe
functional equation
algebra