One to one function basically denotes the mapping of two sets. With the help of examples or solving problems based on this concept, we are going to learn about this function, so that its concept could be easily understood.Â Apart from the onetoone function, there are other sets of functions which denotes the relation between sets, elements or identities. They are;
 Many to One function or Surjective function
 Onto Function or Bijective function
Functions
A function f() is a method, which relates elements/values of one variable to the elements/values of another variable, in such a way that elements of the second variable is identically determined by the elements of the first variable. A function has many types and one of the most common functions used is the onetoone function or injective function. Also, we will be learning here the inverse of this function.
Also, we have other types of functions in Maths which you can learn here easily, such as Identity function, Constant function, Polynomial function, etc. Let us now learn, a brief explanation with definition, its representation and example.
Definition of OnetoOne Functions
OnetoOne functions define that each element of one set say Set (A) is mapped with a unique element of another set, say, Set (B).
Or
ItÂ could be defined as each element of Set A has a unique element on Set B.
In brief, let us consider â€˜fâ€™ is a function whose domain is set A. The function is said to be injective if for all x and y in A,
Whenever f(x)=f(y), then x=y
And equivalently, if x â‰ y, then f(x) â‰ f(y)
Formally, it is stated as, if f(x)=f(y) Â implies x=y, then f is onetoone mapped or f is 11.
Similarly, if f is a function which is one to one, with domain A and range B, then the inverse of function f is given by;
f^{1}(y) = x ; if and only if f(x) = y
Horizontal Line Test: An injective function can be determined by the horizontal line test or geometric test.
 If a horizontal line can intersect the graph of the function, more than one time then the function is not mapped as onetoone.
 If a horizontal line can intersect the graph of the function only a single time, then the function is mapped as onetoone.
Example
Example: Let A = {1, 2, 3} and B = {a, b, c, d}. Which of the following is a onetoone function?
 {1,a1,a, 2,c2,c, 3,a3,a}
 {1,b1,b, 2,d2,d, 3,a3,a}
 {1,a1,a, 2,a2,a, 3,a3,a}
 {1,c1,c, 2,b2,b, 1,a1,a, 3,d3,d}
The Answer is 2.
Explanation: Here, option number 2 satisfies the onetoone condition, as elements of set B(range) is uniquely mapped with elements of set A(domain).
Students are advised to solve more of such example problems,Â to understand the concept of onetoone mapping clearly. To learn more about functions topic, you can visit BYJUâ€™S Maths section, where we have explained all types of functions. Also, download its app to get personalised learning videos.
Related Links 

Domain Codomain Range Functions  
Relations And Functions 