Testing Inverse Relationships Algebraically

If $f (x) = \frac{1}{x + 2}$ and $g (x) = \frac{1}{x} - 2,$ 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.

Your turn

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

If $f (x) = x^{3} - 4$ and $g (x) = \sqrt[3]{x + 4},$ is $g = f^{- 1} ?$

How did it go?