The domain of f(x) is [2, 20) and the range is (-4, 12). What is the domain and range of f^-1(x)

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.

Explore how to determine the domain and range of inverse functions using the example of a function with domain [2, 20) and range (-4, 12). Learn the process of finding inverse functions and the relationship between function domains and ranges. Suitable for advanced high school students and college students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation