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Contests
National and Regional Contests
China Contests
China Team Selection Test
1990 China Team Selection Test
2
Find three functions
Find three functions
Source: China TST 1990, problem 6
June 27, 2005
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
,
g
,
h
:
R
↦
R
f,g,h: \mathbb{R} \mapsto \mathbb{R}
f
,
g
,
h
:
R
↦
R
such that
f
(
x
)
−
g
(
y
)
=
(
x
−
y
)
⋅
h
(
x
+
y
)
f(x) - g(y) = (x-y) \cdot h(x+y)
f
(
x
)
−
g
(
y
)
=
(
x
−
y
)
⋅
h
(
x
+
y
)
for
x
,
y
∈
R
.
x,y \in \mathbb{R}.
x
,
y
∈
R
.
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