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Mathematics
Mathematics
Problem
Let
f
f
f
be a real-valued function defined on the interval
(
−
1
,
1
)
(-1, 1)
(
−
1
,
1
)
such that
e
−
x
f
(
x
)
=
2
+
∫
0
x
t
4
+
1
⋅
d
t
,
∀
x
∈
(
−
1
,
1
)
e^{-x} f(x) = 2 + \int_{0}^{x} \sqrt{t^4 + 1} \cdot dt, \quad \forall x \in (-1, 1)
e
−
x
f
(
x
)
=
2
+
∫
0
x
t
4
+
1
⋅
d
t
,
∀
x
∈
(
−
1
,
1
)
and let
f
−
1
f^{-1}
f
−
1
be the inverse function of
f
f
f
. Then
[
f
−
1
(
2
)
]
′
[f^{-1}(2)]'
[
f
−
1
(
2
)
]
′
is equal to a. 1 b.
1
/
3
1/3
1/3
c.
1
/
2
1/2
1/2
d.
1
/
e
1/e
1/
e
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