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5
f(x)+2f((x+2010)/(x-1))=4020 - x (HOMC 2012 Q5)
f(x)+2f((x+2010)/(x-1))=4020 - x (HOMC 2012 Q5)
Source:
July 24, 2019
algebra
Functional Equations
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a function such that
f
(
x
)
+
2
f
(
x
+
2010
x
−
1
)
=
4020
−
x
f(x)+2f\left(\frac{x+2010}{x-1}\right)=4020 - x
f
(
x
)
+
2
f
(
x
−
1
x
+
2010
)
=
4020
−
x
for all
x
≠
1
x \ne 1
x
=
1
. Then the value of
f
(
2012
)
f(2012)
f
(
2012
)
is(A)
2010
2010
2010
, (B)
2011
2011
2011
, (C)
2012
2012
2012
, (D)
2014
2014
2014
, (E) None of the above.
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