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Byju's Answer
Standard XII
Mathematics
Inverse Function
If the range ...
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
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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
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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 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
]
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