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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
11.2
f(f(x)) = 1 + 2x, f(f(x)) = 1 - 2x (III Soros Olympiad 1996-97 R1 11.2)
f(f(x)) = 1 + 2x, f(f(x)) = 1 - 2x (III Soros Olympiad 1996-97 R1 11.2)
Source:
May 29, 2024
algebra
functional equation
Problem Statement
Is there a function
f
(
x
)
f(x)
f
(
x
)
defined and continuous on
R
R
R
such that:a)
f
(
f
(
x
)
)
=
1
+
2
x
f(f(x)) = 1 + 2x
f
(
f
(
x
))
=
1
+
2
x
? b)
f
(
f
(
x
)
)
=
1
ā
2
x
f(f(x)) = 1 - 2x
f
(
f
(
x
))
=
1
ā
2
x
?
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