MathDB
Problems
Contests
National and Regional Contests
India Contests
ISI B.Stat Entrance Exam
2005 ISI B.Stat Entrance Exam
3
functional equation with two variables
functional equation with two variables
Source: ISI(BS) 2005 #3
May 20, 2012
function
algebra proposed
algebra
Problem Statement
Let
f
f
f
be a function defined on
{
(
i
,
j
)
:
i
,
j
∈
N
}
\{(i,j): i,j \in \mathbb{N}\}
{(
i
,
j
)
:
i
,
j
∈
N
}
satisfying(i)
f
(
i
,
i
+
1
)
=
1
3
f(i,i+1)=\frac{1}{3}
f
(
i
,
i
+
1
)
=
3
1
for all
i
i
i
(ii)
f
(
i
,
j
)
=
f
(
i
,
k
)
+
f
(
k
,
j
)
−
2
f
(
i
,
k
)
f
(
k
,
j
)
f(i,j)=f(i,k)+f(k,j)-2f(i,k)f(k,j)
f
(
i
,
j
)
=
f
(
i
,
k
)
+
f
(
k
,
j
)
−
2
f
(
i
,
k
)
f
(
k
,
j
)
for all
k
k
k
such that
i
<
k
<
j
i <k<j
i
<
k
<
j
.Find the value of
f
(
1
,
100
)
f(1,100)
f
(
1
,
100
)
.
Back to Problems
View on AoPS