MathDB
Problems
Contests
International Contests
IberoAmerican
2022 Iberoamerican
3
Bounded function in (0,1)
Bounded function in (0,1)
Source: Iberoamerican 2022 Day 1, P3
September 29, 2022
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
y
f
(
x
)
)
+
f
(
x
−
1
)
=
f
(
x
)
f
(
y
)
f(yf(x))+f(x-1)=f(x)f(y)
f
(
y
f
(
x
))
+
f
(
x
−
1
)
=
f
(
x
)
f
(
y
)
and
∣
f
(
x
)
∣
<
2022
|f(x)|<2022
∣
f
(
x
)
∣
<
2022
for all
0
<
x
<
1
0<x<1
0
<
x
<
1
.
Back to Problems
View on AoPS