2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Consistency of Linear System of Equations
If f x = ln...
Question
If
f
(
x
)
=
(
ln
x
)
3
a. Write
f
(
x
z
)
in terms of
f
(
x
)
b. From
(
a
)
deduce
f
(
x
n
)
in terms of
k
f
(
x
)
where
k
is perfect cube given
n
is a positive integer
c. Find the derivative of
f
(
x
n
)
at
x
=
n
Open in App
Solution
If
f
(
x
)
=
(
l
n
x
)
3
f
(
x
z
)
=
(
l
n
(
n
z
)
)
3
f
(
x
z
)
=
(
z
l
n
(
x
)
)
3
f
(
x
z
)
=
3
3
f
(
x
)
f
(
x
n
)
=
n
3
f
(
x
)
n
3
=
K
f
(
x
n
)
=
K
f
(
x
)
[where
K
=
n
3
]
d
d
n
(
f
(
n
n
)
)
at
x
=
n
=
d
d
n
[
K
f
(
n
)
]
x
=
4
=
K
d
d
n
f
(
x
)
=
K
f
′
(
n
)
|
x
=
n
=
K
f
′
(
n
)
=
n
3
f
′
(
n
)
=
n
3
(
3
l
n
(
x
)
2
)
1
n
=
3
(
l
n
n
)
2
n
2
Suggest Corrections
0
Similar questions
Q.
Let
f
(
x
1
+
x
2
+
.
.
.
+
x
n
n
)
=
f
(
x
1
)
+
f
(
x
2
)
+
.
.
.
+
f
(
x
n
)
n
where all
x
i
∈
R
are independent to each other and
n
∈
N
. if
f
(
x
)
is differentiable and
f
′
(
0
)
=
a
,
f
(
0
)
=
b
and
f
′
(
x
)
is equal to
Q.
The
8
th
term of
(
3
x
+
2
3
x
2
)
12
when expanded in ascending powers of x, is
a
x
n
,
where a & n are positive integers, Find the value of
(
a
−
n
)
Q.
Find the number of terms in the expansion of
(
x
1
+
x
2
+
x
3
.
.
.
.
x
k
)
n
Q.
The number of positive terms in the sequence
{
X
n
}
,
if
X
n
=
90
7
(
n
P
n
)
−
n
+
4
P
3
n
+
2
P
n
+
2
,
n
∈
N
is
Q.
A function
f
(
x
)
is so defined that for all
x
,
[
f
(
x
)
]
n
=
f
(
n
x
)
. If
f
′
(
x
)
denotes derivative of
f
(
x
)
w.r.t
x
, then show that
f
′
(
x
)
.
f
(
n
x
)
=
f
(
x
)
.
f
′
(
n
x
)
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Consistency of Linear System of Equations
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app