MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
1999 Turkey Team Selection Test
3
f(x-1-f(x)) = f(x)-x-1
f(x-1-f(x)) = f(x)-x-1
Source: Turkey TST 1999 - P3
July 2, 2012
function
algebra proposed
algebra
Problem Statement
Determine all functions
f
:
R
→
R
f:\mathbb{R}\rightarrow \mathbb{R}
f
:
R
→
R
such that the set
{
f
(
x
)
x
:
x
≠
0
and
x
∈
R
}
\left \{ \frac{f(x)}{x}: x \neq 0 \textnormal{ and } x \in \mathbb{R}\right \}
{
x
f
(
x
)
:
x
=
0
and
x
∈
R
}
is finite, and for all
x
∈
R
x \in \mathbb{R}
x
∈
R
f
(
x
−
1
−
f
(
x
)
)
=
f
(
x
)
−
x
−
1
f(x-1-f(x)) = f(x) - x - 1
f
(
x
−
1
−
f
(
x
))
=
f
(
x
)
−
x
−
1
Back to Problems
View on AoPS