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Soros Olympiad in Mathematics
I Soros Olympiad 1994-95 (Rus + Ukr)
11.5
f(x) + f(2x^2 - 1) = 2x + a (I Soros Olympiad 1994-99 Round 2 11.5)
f(x) + f(2x^2 - 1) = 2x + a (I Soros Olympiad 1994-99 Round 2 11.5)
Source:
May 26, 2024
algebra
functional
functional equation
Problem Statement
Is there a function
f
(
x
)
f(x)
f
(
x
)
defined for all
x
x
x
and such that for some
a
a
a
and all
x
x
x
holds the equality
f
(
x
)
+
f
(
2
x
2
ā
1
)
=
2
x
+
a
?
f(x) + f(2x^2 - 1) = 2x + a?
f
(
x
)
+
f
(
2
x
2
ā
1
)
=
2
x
+
a
?
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