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Mathematics
Mathematics
Problem
Let
f
f
f
be a differentiable function with inverse
f
−
1
f^{-1}
f
−
1
. If
f
(
a
)
=
b
f(a)=b
f
(
a
)
=
b
and
f
′
(
a
)
≠
0
f'(a)\neq 0
f
′
(
a
)
=
0
, which of the following gives
(
f
−
1
)
′
(
b
)
(f^{-1})'(b)
(
f
−
1
)
′
(
b
)
in terms of
f
′
(
a
)
f'(a)
f
′
(
a
)
? a)
f
′
(
a
)
f'(a)
f
′
(
a
)
b)
1
f
′
(
b
)
\dfrac{1}{f'(b)}
f
′
(
b
)
1
c)
1
f
′
(
a
)
\dfrac{1}{f'(a)}
f
′
(
a
)
1
d)
f
′
(
b
)
f'(b)
f
′
(
b
)
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