The domain and range of the inverse function $f^{-1}(x)$ are determined by swapping the domain and range of the original function $f(x)$.

Given:

• The domain of $f(x)$ is $[2, 20)$
• The range of $f(x)$ is $(-4, 12)$

For the inverse function $f^{-1}(x)$:

• The domain of $f^{-1}(x)$ is the range of $f(x)$
• The range of $f^{-1}(x)$ is the domain of $f(x)$

Therefore:

• The domain of $f^{-1}(x)$ is $(-4, 12)$
• The range of $f^{-1}(x)$ is $[2, 20)$

If you have any questions or need further details, please let me know. Here are some additional questions you might consider:

1. How do you find the inverse of a function?
2. What are the conditions for a function to have an inverse?
3. How do you graph the inverse of a function?
4. What is the relationship between the derivative of a function and its inverse?
5. How do you determine if a function is one-to-one?

Tip: When finding the inverse of a function, it's helpful to interchange the roles of $x$ and $y$ and solve for the new $y$. This process helps in understanding the relationship between a function and its inverse.