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Poland Contests
Polish MO Finals
1985 Polish MO Finals
3
3
Part of
1985 Polish MO Finals
Problems
(1)
f(3x) = 3f(x) - 4f(x)^3 , continuous at x = 0, prove that |f(x)| \le 1
Source: 1985 Polish MO Finals p3
1/21/2020
The function
f
:
R
→
R
f : R \to R
f
:
R
→
R
satisfies
f
(
3
x
)
=
3
f
(
x
)
−
4
f
(
x
)
3
f(3x) = 3f(x) - 4f(x)^3
f
(
3
x
)
=
3
f
(
x
)
−
4
f
(
x
)
3
for all real
x
x
x
and is continuous at
x
=
0
x = 0
x
=
0
. Show that
∣
f
(
x
)
∣
≤
1
|f(x)| \le 1
∣
f
(
x
)
∣
≤
1
for all
x
x
x
.
function
continuous
inequalities