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.

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
*

*
*

*
gof will be
*

*
*

*
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

gof≠fog.

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