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National and Regional Contests
PEN Problems
PEN K Problems
20
20
Part of
PEN K Problems
Problems
(1)
K 20
Source:
5/25/2007
Find all functions
f
:
Q
→
Q
f: \mathbb{Q}\to \mathbb{Q}
f
:
Q
→
Q
such that for all
x
,
y
∈
Q
x,y \in \mathbb{Q}
x
,
y
∈
Q
:
f
(
x
+
y
)
+
f
(
x
−
y
)
=
2
(
f
(
x
)
+
f
(
y
)
)
.
f(x+y)+f(x-y)=2(f(x)+f(y)).
f
(
x
+
y
)
+
f
(
x
−
y
)
=
2
(
f
(
x
)
+
f
(
y
))
.
function
induction
Functional Equations