MathDB
Problems
Contests
International Contests
Tuymaada Olympiad
2021 Tuymaada Olympiad
1
Too Ez polynomial inequality
Too Ez polynomial inequality
Source: Tuymaada 2021 Senior P1
July 28, 2021
inequalities
Problem Statement
Polynomials
F
F
F
and
G
G
G
satisfy:
F
(
F
(
x
)
)
>
G
(
F
(
x
)
)
>
G
(
G
(
x
)
)
F(F(x))>G(F(x))>G(G(x))
F
(
F
(
x
))
>
G
(
F
(
x
))
>
G
(
G
(
x
))
for all real
x
x
x
.Prove that
F
(
x
)
>
G
(
x
)
F(x)>G(x)
F
(
x
)
>
G
(
x
)
for all real
x
x
x
.
Back to Problems
View on AoPS