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Mathematics
Problem
Let
f
(
x
)
=
2
x
3
+
3
x
f(x)=2x^{3}+3x
f
(
x
)
=
2
x
3
+
3
x
for all real
x
x
x
. The function
f
f
f
is invertible with inverse function
f
−
1
f^{-1}
f
−
1
. (a) Justify that
f
f
f
is invertible on
R
\mathbb{R}
R
. (b) Compute
f
′
(
x
)
f'(x)
f
′
(
x
)
. (c) Using your result from part (b), determine
(
f
−
1
)
′
(
5
)
(f^{-1})'(5)
(
f
−
1
)
′
(
5
)
.
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