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Problems
Contests
National and Regional Contests
Costa Rica Contests
Costa Rica - Final Round
2018 Costa Rica - Final Round
F3
F3
Part of
2018 Costa Rica - Final Round
Problems
(1)
f(2018) =? f has period 5, f(x)=x^2 when x \in [-2,3]
Source:
10/1/2021
Consider a function
f
:
R
→
R
f: R \to R
f
:
R
→
R
that fulfills the following two properties:
f
f
f
is periodic of period
5
5
5
(that is, for all
x
∈
R
x\in R
x
∈
R
,
f
(
x
+
5
)
=
f
(
x
)
f (x + 5) = f (x)
f
(
x
+
5
)
=
f
(
x
)
), and by restricting
f
f
f
to the interval
[
−
2
,
3
]
[-2,3]
[
−
2
,
3
]
,
f
f
f
coincides to
x
2
x^2
x
2
. Determine the value of
f
(
2018
)
.
f(2018).
f
(
2018
)
.
algebra
functions