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If is a polynomial function satisfying and
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem
If
f
(
x
)
f(x)
f
(
x
)
is a polynomial function satisfying
f
(
x
)
f
(
1
x
)
=
f
(
x
)
+
f
(
1
x
)
f(x)f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)
f
(
x
)
f
(
x
1
)
=
f
(
x
)
+
f
(
x
1
)
and
f
(
3
)
=
28
f(3)=28
f
(
3
)
=
28
, then
f
(
4
)
=
f(4)=
f
(
4
)
=
(a) 64 (b) 65 (c) 66 (d) 63
Related theory
Algebraic Identities
Polynomials
Functions
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