1.4 Compositions of Functions

Compositions of Functions is another way of combining two functions. When these two functions form together, they create the composition of one with the other.

The composition of the functions f with g is

 

 

Example 1: Forming the Composition of f with g

• Find the composition function for the following:

 

Example 2: Forming the Composition of g with f

• Find the composition function for the following:





 

Example 3:

• Find the composition function for the following: 
   
  
• If possible, find
  
  

The domain of the composition function is [1, ∞].

So,

is defined, but

is not defined because 0 is not in the domain of

 

 

Example 4: A Case in Which

• Given
   
  
• Find the following:
  a. 
  b.

a.                                                        

 

 

b.

 

So,

 but this isn't always true. There are cases where the two do not equal each other.

 

Practice Problems

 

1. Given

 

Find

a.

b.

 

Answer:

 a.

b.

 

2. Given

 

Find

a.

b.

 

Answer:

a.

b.