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Identity function is a function which gives the same value as inputted.

identity function.jpg

Example

f: X → Y

f(x) = x

Is an identity function

We discuss more about graph of f(x) = x in this post

 


Find identity function of fog and gof

f: X → Y

& g: Y → X

 

gof

gof = g(f(x))

gof : X → X

 

We input x

So, we should get x

gof = x

We write gof = I X

where I X is the identity function in set X

 

fog

fog = f(g(y))

fog : Y → Y

 

We input y

So, we should get y

∴ fog = y

We write fog = I Y

where I Y is the identity function in set Y

 


Find Identity Function of set X and set Y

X = {1, 2, 3}

Y = {4, 5, 6}

 

In identity function,

we get what we input

If we input 1, we should get 1

 

Identity function of set X

If we input 1, we should get 1

If we input 2, we should get 2

If we input 3, we should get 3

 

∴ I X = {(1, 1), (2, 2), (3, 3)}

 

Identity function of set Y

If we input 4, we should get 4

If we input 5, we should get 5

If we input 6, we should get 6

∴ I Y = {(4, 4), (5, 5), (6, 6)}

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.