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Rioplatense Mathematical Olympiad, Level 3
2001 Rioplatense Mathematical Olympiad, Level 3
4
4
Part of
2001 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
f(f(x)-y)f(x+f(y))=x^2-y^2 , f: R \to R$
Source: Rioplatense Olympiad 2001 level 3 P4
9/6/2018
Find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
such that, for any
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
:
f
(
f
(
x
)
−
y
)
⋅
f
(
x
+
f
(
y
)
)
=
x
2
−
y
2
f\left( f\left( x \right)-y \right)\cdot f\left( x+f\left( y \right) \right)={{x}^{2}}-{{y}^{2}}
f
(
f
(
x
)
−
y
)
⋅
f
(
x
+
f
(
y
)
)
=
x
2
−
y
2
functional equation
Find all functions
algebra