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Swedish Mathematical Competition
2012 Swedish Mathematical Competition
1
1
Part of
2012 Swedish Mathematical Competition
Problems
(1)
f(2012)=? if f (x + 1) =(1 + f (x))/ (1 - f (x)) , f(1000)=2012
Source: 2012 Swedish Mathematical Competition p1
4/30/2021
The function
f
f
f
satisfies the condition
f
(
x
+
1
)
=
1
+
f
(
x
)
1
−
f
(
x
)
f (x + 1) = \frac{1 + f (x)}{1 - f (x)}
f
(
x
+
1
)
=
1
−
f
(
x
)
1
+
f
(
x
)
for all real
x
x
x
, for which the function is defined. Determine
f
(
2012
)
f(2012)
f
(
2012
)
, if we known that
f
(
1000
)
=
2012
f(1000)=2012
f
(
1000
)
=
2012
.
algebra
functional equation
functional