Problem #2
Let
F
be a function from the interval [0,1] to itself having the following properties
F
is increasing, i.e.
x
≤
y
implies that
F
(
x
) ≤
F
(
y
).
F
(
x
/3) =
F
(
x
)/2.
F
(
x
) +
F
(1 -
x
) = 1.
Find the following values:
F
(1/13)
F
(Sqrt[1/2])
Source: Nordic Mathematical Contest
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