### Home > PC3 > Chapter 1 > Lesson 1.3.2 > Problem1-123

1-123.

Given $f\left(x\right)=\sqrt[3]{x}+2$

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

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?

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