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Switzerland Contests
Switzerland Team Selection Test
2006 Switzerland Team Selection Test
3
Functional equation
Functional equation
Source: Swiss Imo Selection 2006
May 25, 2006
function
algebra
domain
limit
algebra proposed
Problem Statement
Find all the functions
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
satisfying for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
f
(
f
(
x
)
−
y
2
)
=
f
(
x
)
2
−
2
f
(
x
)
y
2
+
f
(
f
(
y
)
)
f(f(x)-y^2) = f(x)^2 - 2f(x)y^2 + f(f(y))
f
(
f
(
x
)
−
y
2
)
=
f
(
x
)
2
−
2
f
(
x
)
y
2
+
f
(
f
(
y
))
.
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