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National and Regional Contests
Taiwan Contests
TST Round 3
2016 Taiwan TST Round 3
2
Function Equation
Function Equation
Source: 2016 Taiwan TST Round 3
July 25, 2016
function
functional equation
algebra
Problem Statement
Determine all functions
f
:
R
+
→
R
+
f:\mathbb{R}^+\rightarrow \mathbb{R}^+
f
:
R
+
→
R
+
satisfying
f
(
x
+
y
+
f
(
y
)
)
=
4030
x
−
f
(
x
)
+
f
(
2016
y
)
,
∀
x
,
y
∈
R
+
f(x+y+f(y))=4030x-f(x)+f(2016y), \forall x,y \in \mathbb{R}^+
f
(
x
+
y
+
f
(
y
))
=
4030
x
−
f
(
x
)
+
f
(
2016
y
)
,
∀
x
,
y
∈
R
+
.
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