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Brazil National Olympiad
1993 Brazil National Olympiad
5
5
Part of
1993 Brazil National Olympiad
Problems
(1)
F(2x+1) = 3f(x) + 5
Source: Problem 5, Brazil MO 1993
3/18/2006
Find at least one function
f
:
R
ā
R
f: \mathbb R \rightarrow \mathbb R
f
:
R
ā
R
such that
f
(
0
)
=
0
f(0)=0
f
(
0
)
=
0
and
f
(
2
x
+
1
)
=
3
f
(
x
)
+
5
f(2x+1) = 3f(x) + 5
f
(
2
x
+
1
)
=
3
f
(
x
)
+
5
for any real
x
x
x
.
function
logarithms
algebra
functional equation
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