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National and Regional Contests
Moldova Contests
Chisinau City MO
1976 Chisinau City MO
129
Chisinau MO p129 1976 X f(x+\pi)=f(x)/(3f(x)-1)
Chisinau MO p129 1976 X f(x+\pi)=f(x)/(3f(x)-1)
Source:
March 16, 2021
algebra
functional
function
periodic
Problem Statement
The function
f
(
x
)
f (x)
f
(
x
)
satisfies the relation
f
(
x
+
π
)
=
f
(
x
)
3
f
(
x
)
−
1
f(x+\pi)=\frac{f(x)}{3f(x) -1}
f
(
x
+
π
)
=
3
f
(
x
)
−
1
f
(
x
)
for any real number
x
x
x
. Prove that the function
f
(
x
)
f (x)
f
(
x
)
is periodic.
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