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Mathematics
Problem
Suppose
f
f
f
is differentiable and invertible with
f
(
2
)
=
5
f(2)=5
f
(
2
)
=
5
and
f
′
(
2
)
=
−
3
f'(2)=-3
f
′
(
2
)
=
−
3
. Let
g
g
g
be differentiable with
g
′
(
2
)
=
7
g'(2)=7
g
′
(
2
)
=
7
. Define
k
(
x
)
=
g
(
f
−
1
(
x
)
)
k(x)=g\bigl(f^{-1}(x)\bigr)
k
(
x
)
=
g
(
f
−
1
(
x
)
)
. Determine
k
′
(
5
)
k'(5)
k
′
(
5
)
.
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