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Byju's Answer
Standard XII
Mathematics
Change of Variables
The function ...
Question
The
function
f
(
x
)
=
cot
x
is
defined
for
all
x
∈
R
~
n
π
,
n
∈
Z
.
A
True
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B
False
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Solution
The correct option is
A
True
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Similar questions
Q.
The
function
f
(
x
)
=
cot
x
is
defined
for
all
x
∈
R
~
n
π
,
n
∈
Z
.
Q.
The
function
f
(
x
)
=
tan
x
is
defined
for
x
∈
R
~
(
2
n
+
1
)
π
2
,
n
∈
Z
Q.
Let
Z
be the set of integers and
f
:
Z
→
Z
be defined as
f
(
x
)
=
x
2
,
x
∈
Z
, then function 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
)
.
Q.
Let
f
:
Z
→
Z
be a function satisfying
f
(
0
)
≠
0
,
f
(
1
)
=
0
and
f
(
x
y
)
+
f
(
x
)
f
(
y
)
=
f
(
x
)
+
f
(
y
)
;
(
f
(
x
−
y
)
−
f
(
0
)
)
f
(
x
)
f
(
y
)
=
0
,
for all
x
,
y
,
∈
Z
, simultaneously.
(a) Find the set of all possible values of the function
f
.
(b) If
f
(
10
)
≠
0
a
n
d
f
(
2
)
=
0
, find the set of all integers
n
such that
f
(
n
)
≠
0
.
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