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Hanoi Open Mathematics Competition
2018 Hanoi Open Mathematics Competitions
2
2f(x) + f(2 - x) = 5 + x, f(0) + f(2) wanted (HOMC 2018 Ind. p2)
2f(x) + f(2 - x) = 5 + x, f(0) + f(2) wanted (HOMC 2018 Ind. p2)
Source:
January 31, 2020
polynomial
functional equation
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial such that
2
f
(
x
)
+
f
(
2
ā
x
)
=
5
+
x
2f(x) + f(2 - x) = 5 + x
2
f
(
x
)
+
f
(
2
ā
x
)
=
5
+
x
for any real number x. Find the value of
f
(
0
)
+
f
(
2
)
f(0) + f(2)
f
(
0
)
+
f
(
2
)
.A.
4
4
4
B.
0
0
0
C.
2
2
2
D.
3
3
3
E.
1
1
1
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