## Introduction

An identity function is a function with the same output as the input. An identity function is also known as an identity map or relation.

When a function returns the same value as the output used as its input, it is called an identity function.

## Definition

If each element of set A has an image on itself, f (a) = a ∀ a ∈ A, the function f is termed the identity function. It is symbolised by the letter 'I'.

Since the image of elements in domain is identical to the output in the range, it is termed an identity function. As a result, an identity function is a function that directs each actual number to itself. An identity function's output is the same as its input. Since the pre-image and the picture are similar, identity functions are easily detected.

For Example:

Consider, A = { 20, 40, 60, 70, 90 }

f: A → A such that

f = {(20 , 20), (40 , 40), (60 , 60), (70 , 70), (90 , 90)}