Determining Inverse Relationships for Power Functions

If $f (x) = x^{3}$ (the cube function) and $g (x) = \frac{1}{3} x,$ is $g = f^{- 1} ?$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$f (g (x)) = \frac{x^{3}}{27} \neq x$

No, the functions are not inverses.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

If $f (x) = {(x - 1)}^{3} and g (x) = \sqrt[3]{x} + 1,$ is $g = f^{- 1} ?$

How did it go?