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Mathematics
If g (x) is the inverse of f (x) andf '(x)=(1/1+x3), then g' (x) is equal to
Q. If g (x) is the inverse of
f
(x) and
f
′
(
x
)
=
1
+
x
3
1
,
then g' (x) is equal to
1314
174
KEAM
KEAM 2013
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A
g(x)
B
l +g(x)
C
1
+
(
g
−
(
x
)
3
D
1
+
(
g
(
x
)
)
3
1
E
0
Solution:
Given,
g
(
x
)
=
f
−
1
(
x
)
⇒
f
{
g
(
x
)}
=
x
On differentiating, w.r.t.
x
, we get
f
′
{
g
(
x
)}
⋅
g
′
(
x
)
=
1
⇒
g
′
(
x
)
=
f
′
{
g
(
x
)}
1
∵
f
′
(
x
)
=
1
+
x
3
1
(given)
∴
f
′
{
g
(
x
)}
=
1
+
{
g
(
x
)
}
3
1
Now, from Eq. (i), we get
g
′
(
x
)
=
1
+
{
g
(
x
)
}
3