MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1990 Swedish Mathematical Competition
5
5
Part of
1990 Swedish Mathematical Competition
Problems
(1)
f(xy) f( f(y)/x) = 1 , monotonic
Source: 1990 Swedish Mathematical Competition p5
4/2/2021
Find all monotonic positive functions
f
(
x
)
f(x)
f
(
x
)
defined on the positive reals such that
f
(
x
y
)
f
(
f
(
y
)
x
)
=
1
f(xy) f\left( \frac{f(y)}{x}\right) = 1
f
(
x
y
)
f
(
x
f
(
y
)
)
=
1
for all
x
,
y
x, y
x
,
y
.
functional equation
functional
algebra