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Byju's Answer
Standard XI
Mathematics
Composite Function
fx=x-1, -1 ≤...
Question
f
(
x
)
=
{
x
−
1
,
−
1
≤
x
<
0
x
2
,
0
≤
x
≤
1
and
g
(
x
)
=
sin
x
. Consider the function
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
and
h
2
(
x
)
=
|
f
(
g
(
x
)
)
|
Which of the following is not true about
h
1
(
x
)
?
A
It is periodic function with period
π
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B
Range is
[
0
,
1
]
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C
Domain is
R
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D
None of these
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Solution
The correct option is
D
None of these
|
g
(
x
)
|
=
|
sin
x
|
,
∀
x
∈
R
f
(
|
g
(
x
)
|
)
=
{
|
sin
x
|
−
1
,
−
1
≤
|
sin
x
|
<
0
(
|
sin
x
|
)
2
,
0
≤
|
sin
x
|
≤
1
⇒
f
(
|
g
(
x
)
|
)
=
sin
2
x
Clearly,
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
=
sin
2
x
has a period
π
, range
[
0
,
1
]
, and domain
R
Suggest Corrections
0
Similar questions
Q.
f
(
x
)
=
{
x
−
1
,
−
1
≤
x
<
0
x
2
,
0
≤
x
≤
1
and
g
(
x
)
=
sin
x
. Consider the function
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
and
h
2
(
x
)
=
|
f
(
g
(
x
)
)
|
For when
h
1
(
x
)
and
h
2
(
x
)
are identical functions, then which of the following is not true?
Q.
f
(
x
)
=
{
x
−
1
,
−
1
≤
x
<
0
x
2
,
0
≤
x
≤
1
and
g
(
x
)
=
sin
x
. Consider the function
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
and
h
2
(
x
)
=
|
f
(
g
(
x
)
)
|
Which of the following is not true about
h
1
(
x
)
?
Q.
f
(
x
)
=
{
x
−
1
,
−
1
≤
x
<
0
x
2
,
0
≤
x
≤
1
and
g
(
x
)
=
sin
x
. Consider the function
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
and
h
2
(
x
)
=
|
f
(
g
(
x
)
)
|
Which of the following is not true about
h
2
(
x
)
?
Q.
f
(
x
)
=
{
x
−
1
,
−
1
≤
x
<
0
x
2
,
0
≤
x
≤
1
and
g
(
x
)
=
sin
x
. Consider the function
h
1
(
x
)
=
f
(
|
g
(
x
)
|
)
and
h
2
(
x
)
=
|
f
(
g
(
x
)
)
|
For when
h
1
(
x
)
and
h
2
(
x
)
are identical functions, then which of the following is not true?
Q.
Let the function f, g and h be defined as follows :
f
(
x
)
=
x
sin
(
1
x
)
For
−
1
≤
x
≤
1
and
x
≠
0
0
For
x
=
0
g
(
x
)
=
x
2
sin
(
1
x
)
For
−
1
≤
x
≤
1
and
x
≠
0
0
For
x
=
0
h
(
x
)
=
|
x
|
3
For
−
1
≤
x
≤
1
Which of these functions are differentiable at
x
=
0
?
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