MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2013 HMIC
2
2013 HMIC p2 (x - y)(f(x) - f(y)) = f(x - f(y))f(f(x) - y).
2013 HMIC p2 (x - y)(f(x) - f(y)) = f(x - f(y))f(f(x) - y).
Source:
September 20, 2019
functional
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that, for all real numbers
x
,
y
,
x, y,
x
,
y
,
(
x
−
y
)
(
f
(
x
)
−
f
(
y
)
)
=
f
(
x
−
f
(
y
)
)
f
(
f
(
x
)
−
y
)
.
(x - y)(f(x) - f(y)) = f(x - f(y))f(f(x) - y).
(
x
−
y
)
(
f
(
x
)
−
f
(
y
))
=
f
(
x
−
f
(
y
))
f
(
f
(
x
)
−
y
)
.
Back to Problems
View on AoPS