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Slovenia Contests
Slovenia Team Selection Tests
1998 Slovenia Team Selection Test
1
1
Part of
1998 Slovenia Team Selection Test
Problems
(1)
f((x-y)^2)= f(x)^2 -2x f(y)+y^2
Source: Slovenia TST 1998 p1
2/15/2020
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
that satisfy
f
(
(
x
−
y
)
2
)
=
f
(
x
)
2
−
2
x
f
(
y
)
+
y
2
f((x-y)^2)= f(x)^2 -2x f(y)+y^2
f
((
x
−
y
)
2
)
=
f
(
x
)
2
−
2
x
f
(
y
)
+
y
2
for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
functional equation
functional
algebra