How to determine if a function is invertible?
Understand the Problem
The question is asking for the criteria or methods used to determine whether a given function has an inverse function. This involves understanding properties like injectivity and surjectivity as well as practical techniques such as the horizontal line test for functions represented graphically.
Answer
A function is invertible if it is bijective (both one-to-one and onto).
The final answer is that a function is invertible if it is bijective, meaning it is both one-to-one (injective) and onto (surjective).
Answer for screen readers
The final answer is that a function is invertible if it is bijective, meaning it is both one-to-one (injective) and onto (surjective).
More Information
An invertible function has an inverse function that reverses the operation of the original function.
Tips
A common mistake is to check surjectivity or injectivity alone. Always ensure the function is both.
Sources
- Invertible Functions - Definition, Graph, Solved Examples & FAQs - geeksforgeeks.org
- How do you determine if a function is invertible? - Wyzant - wyzant.com
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