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If satisfies for all
MATHEMATICS · Subjective · AoPS · Mathematics · Functions · Functions
Problem
If
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
satisfies
f
(
x
−
1
)
+
f
(
x
+
1
)
=
3
f
(
x
)
f(x-1)+f(x+1)=\sqrt{3}f(x)
f
(
x
−
1
)
+
f
(
x
+
1
)
=
3
f
(
x
)
for all
x
∈
R
x\in\mathbb{R}
x
∈
R
, determine whether
f
(
x
)
f(x)
f
(
x
)
is periodic.
Related theory
Functions
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