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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 3
2022 Nigerian MO round 3
Problem 2
Real functions
Real functions
Source: 2022 Nigerian MO Round 3/Problem 2
May 2, 2022
Problem Statement
If
f
:
R
→
R
f:\mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
satisfies
f
(
x
2
+
f
(
y
)
)
=
y
+
x
f
(
x
)
f(x^2 +f(y))=y+xf(x)
f
(
x
2
+
f
(
y
))
=
y
+
x
f
(
x
)
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
, find
f
(
x
)
f(x)
f
(
x
)
.
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