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Nordic
1993 Nordic
1
1
Part of
1993 Nordic
Problems
(1)
F(x/3) = F(x)/2, F(1-x)=1-F(x), F( 173/1993) ?, F(1/13)?
Source: Nordic Mathematical Contest 1993 #1
10/5/2017
Let
F
F
F
be an increasing real function defined for all
x
,
0
≤
x
≤
1
x, 0 \le x \le 1
x
,
0
≤
x
≤
1
, satisfying the conditions (i)
F
(
x
3
)
=
F
(
x
)
2
F (\frac{x}{3}) = \frac{F(x)}{2}
F
(
3
x
)
=
2
F
(
x
)
. (ii)
F
(
1
−
x
)
=
1
−
F
(
x
)
F(1- x) = 1 - F(x)
F
(
1
−
x
)
=
1
−
F
(
x
)
. Determine
F
(
173
1993
)
F(\frac{173}{1993})
F
(
1993
173
)
and
F
(
1
13
)
F(\frac{1}{13})
F
(
13
1
)
.
functional equation
increasing functions
algebra