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2022 District Olympiad
P4
Romania District MO 2022 Grade 10 P4
Romania District MO 2022 Grade 10 P4
Source: Romania District MO 2022 Grade 10
March 28, 2022
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
which satisfy the following relationship for all
x
,
y
∈
R
:
x,y\in\mathbb{R}:
x
,
y
∈
R
:
f
(
f
(
y
−
x
)
−
x
f
(
y
)
)
+
f
(
x
)
=
y
⋅
(
1
−
f
(
x
)
)
.
f(f(y-x)-xf(y))+f(x)=y\cdot(1-f(x)).
f
(
f
(
y
−
x
)
−
x
f
(
y
))
+
f
(
x
)
=
y
⋅
(
1
−
f
(
x
))
.
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