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Italy Contests
ITAMO
1997 ITAMO
2
2
Part of
1997 ITAMO
Problems
(1)
f(10+x) = f(10- x) and f(20+x) = - f(20- x), odd and periodic wanted
Source: 1997 ITAMO p2
1/25/2020
Let a real function
f
f
f
defined on the real numbers satisfy the following conditions: (i)
f
(
10
+
x
)
=
f
(
10
−
x
)
f(10+x) = f(10- x)
f
(
10
+
x
)
=
f
(
10
−
x
)
(ii)
f
(
20
+
x
)
=
−
f
(
20
−
x
)
f(20+x) = - f(20- x)
f
(
20
+
x
)
=
−
f
(
20
−
x
)
for all
x
x
x
. Prove that f is odd and periodic.
odd
function
periodic
periodic function
algebra