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National and Regional Contests
Taiwan Contests
TST Round 1
2019 Taiwan TST Round 1
1
Functional equation 013
Functional equation 013
Source: 2019 Taiwan TST Round 1, Day 3, Problem 1
April 14, 2019
function
algebra
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
f
(
y
)
−
f
(
x
)
−
y
)
=
y
f
(
x
)
−
f
(
y
)
−
x
f\left(xf\left(y\right)-f\left(x\right)-y\right) = yf\left(x\right)-f\left(y\right)-x
f
(
x
f
(
y
)
−
f
(
x
)
−
y
)
=
y
f
(
x
)
−
f
(
y
)
−
x
holds for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
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