Given the following functions:

f(x)=x2
g(x)=x−3

find the composition of the two functions and show your process:

f(g(x))

*** caution: this is different from
g(f(x))

2. given the following functions:

f(x)=x2
g(x)=x−3

find the composition of the two functions and show your process:

g(f(x))

caution: this is different from
f(g(x))

3. if the composition of two functions is:

1x−3

what would be the domain restriction? describe how you found that answer.

1) and  are not equal

ie,

2) The domain is x

Step-by-step explanation:

Given functions are and

now find the composition of two functions verify that

now find the composition of  

now find the composition of  

Comparing the above two compositions we get

and   are not equal

ie, .

2) Given that the composition of two function is x-3

Let the functons be f(x) and g(x)

so the composition of two function  

it may be written as

Step-by-step explanation:

Let the age of Seema = P years old

1 / 4 of the age of Seema = 1 / 4 P years old

Seema's little sister = 5 years old

Seema's little sister

= ( 2 + 1 / 4 P ) years old

Equation ==>

2 + 1 / 4 P = 5

1 / 4 P = 5 - 2

1 / 4 P = 3

P = 3 ÷ 1 / 4

P = 3 × 4

P = 12

Seema is years old.

= P

= 12 years old