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Standard XII
Mathematics
Derivative of One Function w.r.t Another
Let f:1,2,3-1...
Question
Let f:{1,2,3}-{1,2,3} be a function. If the number of functions g: {1,2,3}-{1,2,3}. Such that f(x)=g(x) for atleast one x belongs to {1,2,3} is k, then (k-10) is equal to?
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Q.
The number of onto functions
f
from
{
1
,
2
,
3
,
.
.
.
.
,
20
}
to
{
1
,
2
,
3
,
.
.
.
,
20
}
such that
f
(
k
)
is a multiple of
3
, whenever
k
is a multiple of
4
, is :
Q.
Let f: {1, 2, 3} → {1, 2, 3} be an onto function. Then, f is
Q.
The number of functions f from
{
1
,
2
,
3
,
.
.
.20
}
onto
{
1
,
2
,
3
,
.
.
.
,
20
}
such that
f
(
k
)
is a multiple of
3
, whenever k is a multiple of
4
, is:
Q.
Let
g
(
x
)
=
log
(
f
(
x
)
)
where
f
(
x
)
is a twice differentiable positive function on
(
0
,
∞
)
such that
f
(
x
+
1
)
=
x
f
(
x
)
. Then, for
N
=
1
,
2
,
3
,
…
g
′′
(
N
+
1
2
)
−
g
′′
(
1
2
)
=
Q.
Let
A
=
{
1
,
2
,
3
}
,
B
=
{
4
,
5
,
6
,
7
}
and let
f
=
{
(
1
,
4
)
,
(
2
,
5
)
,
(
3
,
6
)
}
be a function from
A
to
B
.Show that
f
is one-one.
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