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3
find f(x)=ax^2+bx+c, if a \ne 0 and f(f(1)) = f(f(0)) = f(f(-1))
find f(x)=ax^2+bx+c, if a \ne 0 and f(f(1)) = f(f(0)) = f(f(-1))
Source: Irmo 2018 p1 q3
September 16, 2018
algebra
trinomial
quadratic trinomial
Problem Statement
Find all functions
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 + bx + c
f
(
x
)
=
a
x
2
+
b
x
+
c
, with
a
≠
0
a \ne 0
a
=
0
, such that
f
(
f
(
1
)
)
=
f
(
f
(
0
)
)
=
f
(
f
(
−
1
)
)
f(f(1)) = f(f(0)) = f(f(-1))
f
(
f
(
1
))
=
f
(
f
(
0
))
=
f
(
f
(
−
1
))
.
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