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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
If f:[2, ∞→ [...
Question
If
f
:
[
2
,
∞
)
→
[
1
,
∞
)
is defined by
f
(
x
)
=
2
x
4
−
4
x
2
,
then
f
−
1
(
x
)
is
A
√
2
+
√
4
+
log
2
x
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B
−
√
2
+
√
4
+
log
2
x
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C
log
e
(
x
4
−
4
x
2
)
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D
log
2
(
x
4
−
4
x
2
)
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Solution
The correct option is
A
√
2
+
√
4
+
log
2
x
y
=
f
(
x
)
=
2
x
4
−
4
x
2
⇒
log
2
y
=
x
4
−
4
x
2
⇒
(
x
2
)
2
−
4
(
x
2
)
−
log
2
y
=
0
⇒
x
2
=
4
±
√
16
+
4
log
2
y
2
⇒
x
2
=
2
+
√
4
+
log
2
y
(
∵
x
≥
2
and
y
≥
1
)
⇒
x
=
√
2
+
√
4
+
log
2
y
⇒
f
−
1
(
y
)
=
√
2
+
√
4
+
log
2
y
Hence,
f
−
1
(
x
)
=
√
2
+
√
4
+
log
2
x
Suggest Corrections
0
Similar questions
Q.
Let
f
:
[
2
,
∞
)
→
[
1
,
∞
)
defined by
f
(
x
)
=
2
x
4
−
4
x
2
and
g
:
[
π
2
,
π
]
→
A
defined by
g
(
x
)
=
sin
x
+
4
sin
x
−
2
be two invertible functions, then
The domain of
f
−
1
g
−
1
(
x
)
is
Q.
If the function
f
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[
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,
∞
)
→
[
1
,
∞
)
is defined by
f
(
x
)
=
3
x
(
x
−
1
)
then
f
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1
(
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is
Q.
Let
f
[
−
1
,
−
1
2
]
→
[
−
1
,
1
]
is defined by
f
(
x
)
=
4
x
3
−
3
x
, then
f
−
1
(
x
)
=
____ .
Q.
f
:
(
−
∞
,
∞
)
→
(
−
∞
,
∞
)
is defined by
f
(
x
)
=
x
(
x
−
1
)
(
x
−
2
)
. Then
f
is
Q.
If
f
:
(
−
1
,
1
)
→
(
−
3
,
3
)
defined by
f
(
x
)
=
cos
(
cos
−
1
x
)
+
sin
(
sin
−
1
x
)
−
tan
(
tan
−
1
x
)
, then
f
is
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