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Mathematics
Problem
Let
f
(
x
)
=
a
x
3
+
b
x
f(x)=ax^{3}+bx
f
(
x
)
=
a
x
3
+
b
x
where
a
≠
0
a\neq 0
a
=
0
and
b
≠
0
b\neq 0
b
=
0
. The function is strictly increasing and thus invertible. Derive a simplified expression for
(
f
−
1
)
′
(
x
)
(f^{-1})'(x)
(
f
−
1
)
′
(
x
)
in terms of
a
a
a
,
b
b
b
, and
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
.
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