Given $f\left(x\right)=\sqrt[3]{x}+2$. 

1. Write an equation for $f^{-1}$.

   Hint (a):

   Change $f(x)$ to $y$.
   Switch every $x$ to $y$ and every $y$ to $x$.
   Solve for $y$.

2. Sketch $y=f(x)$ and $y=f^{-1}(x)$ on the same set of axes.

3. What are $f^{-1}(f(6))$ and $f(f^{-1}(2))$? What do you notice?

   Answer (c):

   Composing $f$ and $f^{−1}$ in either order returns the original number.