Types of functions — lesson. Mathematics State Board, Class 10.

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The functions are of four types, namely:

1. One-to-one function

2. Many-to-one function

3. Onto function

4. Into function

Let us look at each of the functions in detail.

One-to-one function

Let

$f : A \rightarrow B$ be a one-one function. Then, each distinct element in

$A$ will have a distinct image in

$B$ .

Let us look at the representation given below for a better understanding.

In other words, if for all

$a_1$ ,

$a_2$

$\in A$ ,

$f(a_1) = f(a_2)$ implies

$a_1 = a_2$ ,

$f$ is a one-to-one function.

A one-to-one function is otherwise called an injection.

Many-to-one function

Let

$f : A \rightarrow B$ be a many-to-one function. Then, two or more elements in

$A$ will have a distinct image in

$B$ .

Onto function

A function

$f : A \rightarrow B$ is said to be onto function if the range of

$f$ is equal to the co-domain of

$f$ .

That is, every co-domain will have a preimage.

An onto function is also called a surjection.

Into function

A function

$f : A \rightarrow B$ is called an into a function if there exists at least one element in

$B$ which is not the image of any element of

$A$ .

Did you find an error?

3. Types of functions