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Albania IMO TST 2009 Question 2
Albania IMO TST 2009 Question 2
Source:
June 4, 2010
function
algebra
polynomial
induction
calculus
derivative
limit
Problem Statement
Find all the functions
f
:
R
↦
R
f :\mathbb{R}\mapsto\mathbb{R}
f
:
R
↦
R
with the following property:
∀
x
\forall x
∀
x
f
(
x
)
=
f
(
x
/
2
)
+
(
x
/
2
)
f
′
(
x
)
f(x)= f(x/2) + (x/2)f'(x)
f
(
x
)
=
f
(
x
/2
)
+
(
x
/2
)
f
′
(
x
)
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