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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
k
x
3
f(x)=k x^{3}
f
(
x
)
=
k
x
3
, where
k
≠
0
k\neq 0
k
=
0
. Given that
(
f
−
1
)
′
(
8
)
=
1
12
(f^{-1})'(8)=\dfrac{1}{12}
(
f
−
1
)
′
(
8
)
=
12
1
, determine the value of
k
k
k
. a)
k
=
1
16
\displaystyle k=\dfrac{1}{16}
k
=
16
1
b)
k
=
16
\displaystyle k=16
k
=
16
c)
k
=
1
\displaystyle k=1
k
=
1
d)
k
=
8
\displaystyle k=8
k
=
8
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