## About "Composition of two functions examples"

Composition of two functions examples :

Here we are going to see how to find composition of two functions.

We follow the steps given below to find the composition of two functions f with g

Step 1 :

If f(x)  = x and g(x)  =  3x2

fₒ g (x)  =  f [ g(x) ] Step 2 :

In this step we have to apply the value 3x2 instead of x in the function f (x).

f(3x2)  =  3x2

Step 3 :

The answer that we got in step 2 represents the composition of two functions. If it is possible we have to simplify the answer in step 2.

That is,

fₒ g (x) =  3x2

Let us look into some examples to understand the above concept.

## Composition of two functions examples

Example 1 :

If f(x)  =  -4x + 2 and g(x)  =  √(x- 8) find fₒ g (x)

Solution :

Given : f(x)  =  -4x + 2 and g(x)  =  √(x- 8)

Step 1 :

fₒ g (x)  =  f [g(x)]

By applying the value of g(x) in the above step, we get

=  f [ √(x- 8)]

Step 2 :

Now we have to apply x = √(x- 8) in the function of f (x).

=  f(√(x- 8))  =  -4√(x- 8) + 2

Step 3 :

We cannot simplify -4√(x- 8) + 2 here after.

Hence the value of fₒ g (x) is  -4√(x- 8) + 2

Let us look into the next example on "Composition of two functions examples".

Example 2 :

If f(x)  =  -3x + 4 and g(x)  =  x2 find g ₒ f (x)

Solution :

Given : f(x)  =  -3x + 4 and g(x)  =  x2

g ₒ f (x)  =  g [f(x)]

=  g (-3x + 4)

Here x = -3x + 4. Now we are going to apply this value in the function g(x).

g(-3x + 4)  =  (-3x + 4)2

We may expand this using algebraic identity

=  (-3x)2 + 2 (-3x) (4) + 42

=  9x2 - 24x + 16

Hence the value of  g ₒ f (x) is 9x2 - 24x + 16

Example 3 :

If f(x)  =  2x - 5 and g(x)  =  x + 2 find f ₒ g (x)

Solution :

Given : f(x)  =  2x - 5 and g(x)  =  x + 2

ₒ g (x)  =  f [g(x)]

=  f [x + 2]

In the function f(x), we have to apply x + 2 instead of x.

f(x + 2)  =  2(x + 2) - 5

=  2x + 4 - 5

=  2x - 1

Hence the value of ₒ g (x) is 2x - 1.

Example 4 :

If f(x)  =  -9x + 3 and g(x)  =  x4 find g ₒ f (x)

Solution :

Given : f(x)  =  -9x + 3 and g(x)  =  x4

ₒ f (x)  =  g [f(x)]

=  g [-9x + 3]

In the function g(x), we have to apply -9x + 3 instead of x.

g(-9x + 3)  =  (-9x + 3)4

Hence the value of g ₒ f (x) is (-9x + 3)4 After having gone through the stuff given above, we hope that the students would have understood "Composition of two functions examples".

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