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If is a polynomial function satisfying and if
MATHEMATICS · Subjective · AoPS · Mathematics · Functions · Functions
Problem
If
f
f
f
is a polynomial function satisfying
2
+
f
(
x
)
⋅
f
(
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
,
∀
x
,
y
∈
R
2 + f(x) \cdot f(y) = f(x) + f(y) + f(xy), \forall x, y \in R
2
+
f
(
x
)
⋅
f
(
y
)
=
f
(
x
)
+
f
(
y
)
+
f
(
x
y
)
,
∀
x
,
y
∈
R
and if
f
(
2
)
=
5
f(2) = 5
f
(
2
)
=
5
, find
f
(
f
(
2
)
)
f(f(2))
f
(
f
(
2
))
.
Related theory
Functions
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