Problem
If

\[ f(x) = 2x^3  5)\]

, find the inverse

\[f^{1}\]

of f(x).

Solution
Let y = 2x^3  5. Then y + 5 = 2x^3.
So,

\[x^3 = \frac{y + 5}{2}\]

Then,

\[x = \sqrt[3]{\frac {y +5}{2}}\]

Therefore,

\[f^{1}(y) = \sqrt[3]{\frac {y +5}{2}}\]
