Math Problem Statement
Based on the query submitted by the user and the corresponding solution, generate the following information in JSON format.
Solution
To solve this problem, we need to identify the inverse points of the function . For the inverse , the - and -coordinates are swapped. So for each point on , the corresponding point on is .
Points from the graph:
Corresponding points for :
- For : inverse is
- For : inverse is
- For : inverse is
- For : inverse is
Table filled:
Let me know if you'd like further explanation or more examples!
Related Questions:
- What is the geometric relationship between a function and its inverse on the graph?
- How can you verify whether two points are inverses of each other mathematically?
- What happens to the domain and range when a function is inverted?
- Are all functions invertible? Why or why not?
- How does the line relate to the graph of a function and its inverse?
Tip:
For quick inversion, remember to interchange and , but ensure the function is one-to-one before assuming an inverse exists!
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Coordinate Geometry
Formulas
f^{-1}(x): Swap x and y coordinates
Theorems
Inverse of a function
Graphical relationship of functions and their inverses
Suitable Grade Level
Grades 9-12