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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2002 Switzerland Team Selection Test
5
5
Part of
2002 Switzerland Team Selection Test
Problems
(1)
functional eq.
Source: Swiss 2002
10/12/2006
Find all
f
:
R
→
R
f: R\rightarrow R
f
:
R
→
R
such that (i) The set
{
f
(
x
)
x
∣
x
∈
R
−
{
0
}
}
\{\frac{f(x)}{x}| x\in R-\{0\}\}
{
x
f
(
x
)
∣
x
∈
R
−
{
0
}}
is finite (ii)
f
(
x
−
1
−
f
(
x
)
)
=
f
(
x
)
−
1
−
x
f(x-1-f(x)) = f(x)-1-x
f
(
x
−
1
−
f
(
x
))
=
f
(
x
)
−
1
−
x
for all
x
x
x
function
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algebra unsolved
algebra