MathDB
Problems
Contests
International Contests
Rioplatense Mathematical Olympiad, Level 3
2000 Rioplatense Mathematical Olympiad, Level 3
6
6
Part of
2000 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
No functions
Source: Rioplatense Olympiad
3/4/2018
Let
g
(
x
)
=
a
x
2
+
b
x
+
c
g(x) = ax^2 + bx + c
g
(
x
)
=
a
x
2
+
b
x
+
c
a quadratic function with real coefficients such that the equation
g
(
g
(
x
)
)
=
x
g(g(x)) = x
g
(
g
(
x
))
=
x
has four distinct real roots. Prove that there isn't a function
f
f
f
:
R
−
−
R
R--R
R
−
−
R
such that
f
(
f
(
x
)
)
=
g
(
x
)
f(f(x)) = g(x)
f
(
f
(
x
))
=
g
(
x
)
for all
x
x
x
real
function
algebra
algebra unsolved