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National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
2007 Vietnam Team Selection Test
4
find continuous function
find continuous function
Source: Vietnam TST 2007
April 8, 2007
function
algebra proposed
algebra
Problem Statement
Find all continuous functions
f
:
R
→
R
f: \mathbb{R}\to\mathbb{R}
f
:
R
→
R
such that for all real
x
x
x
we have
f
(
x
)
=
f
(
x
2
+
x
3
+
1
9
)
.
f(x)=f\left(x^{2}+\frac{x}{3}+\frac{1}{9}\right).
f
(
x
)
=
f
(
x
2
+
3
x
+
9
1
)
.
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