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

identity function.jpg


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 = 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 = 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.