1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Range
the range of ...
Question
If the range of functions
f
(
x
)
=
(
cos
−
1
x
3
)
2
+
π
sin
−
1
x
3
−
(
sin
−
1
x
3
)
2
+
π
2
4
(
x
2
+
2
x
+
1
)
is
[
a
,
b
]
. then the value of
b
a
is
Open in App
Solution
Let
sin
−
1
(
x
3
)
=
t
and
g
(
x
)
=
(
cos
−
1
x
3
)
2
+
π
sin
−
1
x
3
−
(
sin
−
1
x
3
)
2
⇒
g
(
x
)
=
(
π
2
−
t
)
2
+
π
t
−
t
2
⇒
g
(
x
)
=
π
2
4
⇒
f
(
x
)
=
π
2
4
(
(
x
+
1
)
2
+
1
)
Now
−
1
≤
x
3
≤
1
⇒
−
3
≤
x
≤
3
⇒
−
2
≤
x
+
1
≤
4
⇒
0
≤
(
x
+
1
)
2
≤
16
⇒
1
≤
(
x
+
1
)
2
+
1
≤
17
⇒
π
2
4
≤
π
2
4
(
(
x
+
1
)
2
+
1
)
≤
17
π
2
4
Suggest Corrections
0
Similar questions
Q.
If the range of functions
f
(
x
)
=
(
cos
−
1
x
3
)
2
+
π
sin
−
1
x
3
−
(
sin
−
1
x
3
)
2
+
π
2
4
(
x
2
+
2
x
+
1
)
is
[
a
,
b
]
. then the value of
b
a
is
Q.
If the range of
f
(
x
)
=
sin
−
1
x
+
tan
−
1
x
+
cos
−
1
x
is
=
[
π
a
,
b
π
c
]
,
Find the value of
a
+
b
+
c
Q.
Range of
f
(
x
)
=
tan
−
1
[
2
π
(
2
tan
−
1
x
−
sin
−
1
x
+
cot
−
1
x
−
cos
−
1
x
)
]
contains
Q.
Assertion :Statement 1 Range of
f
(
x
)
=
tan
−
1
x
+
sin
−
1
x
+
cos
−
1
x
is
(
0
,
π
)
Reason: Statement 2
f
(
x
)
=
tan
−
1
x
+
sin
−
1
x
+
cos
−
1
x
=
π
2
+
tan
−
1
x
for
x
ϵ
(
−
1
,
1
]
Q.
The range of
f
(
x
)
=
sin
−
1
x
−
cos
−
1
x
is
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
Plantae
MATHEMATICS
Watch in App
Explore more
Range
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
AI Tutor
Textbooks
Question Papers
Install app