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MHT CET 2017 Math Solved Paper
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© examsnet.com
Question : 7
Total: 50
If g(x) is the inverse function of f(x) and
f
′
(x) =
1
1
+
x
4
, then g’(x) is
1
+
[
g
(
x
)
]
4
1
−
[
g
(
x
)
]
4
1
+
[
f
(
x
)
]
4
1
1
+
[
g
(
x
)
]
4
Validate
Solution:
(a) Given, g(x) =
f
−
1
(
x
)
f(g(x)) = x
On differentiating both sides w.r.t. ‘x’, we get
f(g(x)) - g'(x) = 1
∴
1
1
+
(
g
(
x
)
)
4
g
′
(
x
)
=
1
[
∵
f
′
(
x
)
=
1
1
+
x
4
]
⇒ g'(x) = 1 +
[
g
(
x
)
]
4
© examsnet.com
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