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Brazil National Olympiad
1989 Brazil National Olympiad
3
3
Part of
1989 Brazil National Olympiad
Problems
(1)
Integer to integer functions
Source: 11th Brazilian Math Olympiad - Problem 3
12/27/2017
A function
f
f
f
, defined for the set of integers, is such that
f
(
x
)
=
x
−
10
f(x)=x-10
f
(
x
)
=
x
−
10
if
x
>
100
x>100
x
>
100
and
f
(
x
)
=
f
(
f
(
x
+
11
)
)
f(x)=f(f(x+11))
f
(
x
)
=
f
(
f
(
x
+
11
))
if
x
≤
100
x \leq 100
x
≤
100
.Determine, justifying your answer, the set of all possible values for
f
f
f
.
Brazilian Math Olympiad
Brazilian Math Olympiad 1989
functions
algebra