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Putnam
2000 Putnam
4
Putnam 2000 B4
Putnam 2000 B4
Source:
September 6, 2011
Putnam
function
trigonometry
induction
college contests
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a continuous function such that
f
(
2
x
2
−
1
)
=
2
x
f
(
x
)
f(2x^2-1)=2xf(x)
f
(
2
x
2
−
1
)
=
2
x
f
(
x
)
for all
x
x
x
. Show that
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
for
−
1
≤
x
≤
1
-1\le x \le 1
−
1
≤
x
≤
1
.
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