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All-Russian Olympiad Regional Round
1994 All-Russian Olympiad Regional Round
11.6
(x-1)f )( x+1)/(x−1) )- f(x) = x All-Russian MO 1994 Regional (R4) 11.6
(x-1)f )( x+1)/(x−1) )- f(x) = x All-Russian MO 1994 Regional (R4) 11.6
Source:
August 26, 2024
algebra
functional
Problem Statement
Find all functions satisfying the equality
(
x
−
1
)
f
(
x
+
1
x
−
1
)
−
f
(
x
)
=
x
(x-1)f \left(\dfrac{x+1}{x-1}\right)- f(x) = x
(
x
−
1
)
f
(
x
−
1
x
+
1
)
−
f
(
x
)
=
x
for all
x
≠
1
x \ne 1
x
=
1
.
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