https://file.aiquickdraw.com/mathbot/file/1726912263041vwodzb0k.jpg

The image asks whether the blue graph, representing \( f(x) \), and the red graph, representing \( g(x) \), are inverses of each other.

### To determine if two functions are inverses:
1. The graphs of two inverse functions are reflections of each other across the line \( y = x \).
2. In particular, the coordinates of any point on \( f(x) \) should switch when mapped onto \( g(x) \). If \( f(a) = b \), then for inverse functions, \( g(b) = a \).

### Observations:
- The blue line seems to have a slope of 1 and passes through the points \((-1, -2)\) and \( (2, 3) \).
- The red line seems to pass through the points \((-2, -1)\) and \( (3, 2) \), indicating a reflection across the line \( y = x \).

Because the graphs are symmetric with respect to the line \( y = x \), it confirms that the functions are indeed inverses of each other.

### Conclusion:
The correct answer is **True**.

---

Would you like more details on inverse functions or have any other questions? 

Here are 5 related questions you might find interesting:
1. How do you algebraically verify if two functions are inverses of each other?
2. What happens to the domain and range when dealing with inverse functions?
3. What properties do inverse functions share with each other?
4. How can you use function composition to verify that two functions are inverses?
5. Why is the line \( y = x \) important when analyzing inverse functions?

**Tip:** The composition of a function and its inverse will always result in the identity function: \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Consider the blue graph as f(x) and the red graph as g(x). From the graph below, the functions f and g are inverses.

Learn how to determine if two functions are inverses by analyzing the symmetry of their graphs across the line y = x. In this problem, we explore whether the blue graph representing f(x) and the red graph representing g(x) are inverses of each other. This problem is ideal for high school students (Grades 9-12) learning about inverse functions and graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation