One to One Functions

1. What is a one-to-one function?

A one-to-one function is a mathematical function that maps each element in its domain to a unique element in its codomain. In other words, it doesn’t map two different elements in the domain to the same element in the codomain.

2. How can I determine if a function is one-to-one?

You can use the horizontal line test. If no horizontal line intersects the graph of the function more than once, it is a one-to-one function.

3. What is the difference between a one-to-one function and an onto function?

A one-to-one function ensures that no two distinct elements in the domain map to the same element in the codomain, while an onto function, also known as a surjective function, ensures that every element in the codomain is mapped to by at least one element in the domain.

4. Are all linear functions one-to-one?

No, not all linear functions are one-to-one. For example, f(x) = 2x is one-to-one, but g(x) = 2x + 1 is not because it maps two different x-values to the same y-value (e.g., g(1) = 3 and g(2) = 5).

One to One Function or One-One Function is one of the types of functions defined over domain and codomain and describes the specific type of relationship between domain and the codomain. One to One Function is also called the Injective Function. One to One Function is a mathematical function where each element in the domain maps to a unique element in the codomain.

This article explores the concept of One to One Function or One-One Function in detail including its definition and examples which help you understand the concept with ease. We will also discuss some sample problems and provide some practice problems for you to solve. So, let’s learn about this important concept in mathematics known as One to One Function.