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2021 Romania Team Selection Test
4
Romania TST 2021 Day 1 P4
Romania TST 2021 Day 1 P4
Source:
May 15, 2021
algebra
function
Romanian TST
TST
Problem Statement
Determine all functions
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
which satisfy the following relationship for all real numbers
x
x
x
and
y
y
y
f
(
x
f
(
y
)
−
f
(
x
)
)
=
2
f
(
x
)
+
x
y
.
f(xf(y)-f(x))=2f(x)+xy.
f
(
x
f
(
y
)
−
f
(
x
))
=
2
f
(
x
)
+
x
y
.
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