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Nordic
1998 Nordic
1
1
Part of
1998 Nordic
Problems
(1)
f(x + y) + f(x − y) = 2f(x) + 2f(y) in Q
Source: Nordic Mathematical Contest 1998 #1
10/3/2017
Determine all functions
f
f
f
defined in the set of rational numbers and taking their values in the same set such that the equation
f
(
x
+
y
)
+
f
(
x
ā
y
)
=
2
f
(
x
)
+
2
f
(
y
)
f(x + y) + f(x - y) = 2f(x) + 2f(y)
f
(
x
+
y
)
+
f
(
x
ā
y
)
=
2
f
(
x
)
+
2
f
(
y
)
holds for all rational numbers
x
x
x
and
y
y
y
.
functional equation
rational function
function
algebra