MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia TST
2010 Indonesia TST
1
xf(y) - yf(x) = f (y/x), probably known
xf(y) - yf(x) = f (y/x), probably known
Source: 2010 Indonesia TST stage 2 test 1 p1
December 16, 2020
algebra
functional
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
that satisfies
x
f
(
y
)
−
y
f
(
x
)
=
f
(
y
x
)
xf(y) - yf(x)= f\left(\frac{y}{x}\right)
x
f
(
y
)
−
y
f
(
x
)
=
f
(
x
y
)
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
Back to Problems
View on AoPS