Check sibling questions

If f: A → B, g: B → C

Then

gof : A → C

gof = g(f(x))

Here, gof is formed by the composition of functions f and g.

Composition of functions.jpg

In gof :

  • Value of x is coming from set A
  • Value of function gof will be from set C

Let us take an example

 

Let f: {1, 2, 3, 4} → {5, 6, 7, 8}

f(1) = 5, f(2) = 6, f(3) = 7, f(4) = 8

and

g: {5, 6, 7, 8} → {9, 10, 11, 12}

g(5) = 9, g(6) = 10, g(7) = 11, g(8) = 12

Find gof

Composition of functions - Part 2

 

gof will be

Composition of functions - Part 3

gof (1) = 10

gof (2) = 11

gof (3) = 12

gof (4) = 13

 


Let’s take another example

f: R R , g: R R

f(x) = sin x , g(x) = x 3

 

Find fog and gof

 

f(x) = sin x

f(g(x)) = sin g(x)

f og (x) = sin (x 3 )

 

g(x) = x 3

g(f(x)) = f(x) 3

go f (x) = sin 3 x

 

Note that go f f og .

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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.