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Swedish Mathematical Competition
2014 Swedish Mathematical Competition
3
3
Part of
2014 Swedish Mathematical Competition
Problems
(1)
f (f (x + y) - f (x - y)) = xy
Source: 2014 Swedish Mathematical Competition p3
4/30/2021
Determine all functions
f
:
R
→
R
f: \mathbb R \to \mathbb R
f
:
R
→
R
, such that
f
(
f
(
x
+
y
)
−
f
(
x
−
y
)
)
=
x
y
f (f (x + y) - f (x - y)) = xy
f
(
f
(
x
+
y
)
−
f
(
x
−
y
))
=
x
y
for all real
x
x
x
and
y
y
y
.
algebra
functional equation
functional