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Putnam
2001 Putnam
5
Putnam 2001 B5
Putnam 2001 B5
Source:
February 27, 2012
Putnam
function
college contests
Problem Statement
Let
a
a
a
and
b
b
b
be real numbers in the interval
(
0
,
1
2
)
\left(0,\tfrac{1}{2}\right)
(
0
,
2
1
)
, and let
g
g
g
be a continuous real-valued function such that
g
(
g
(
x
)
)
=
a
g
(
x
)
+
b
x
g(g(x))=ag(x)+bx
g
(
g
(
x
))
=
a
g
(
x
)
+
b
x
for all real
x
x
x
. Prove that
g
(
x
)
=
c
x
g(x)=cx
g
(
x
)
=
c
x
for some constant
c
c
c
.
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