Chapter 1: Functions and Their Graphs

Compositions of Functions

Just like arithmetic combinations of functions, you can also combine 2 functions by forming the composition of one with the other. In simpler terms, you take the f "of" g "of" x.

Example 1:

Solve for  

Given:

Solution:

To solve this problem, you substitute g(x) into f(x). 

Simplify:

Since you can plug one function into another, you can respectively plug a function into itself as well. 

Example 2: 

Solve for 

Given

To solve this problem, you plug the function into itself and take the g "of" g "of" x

*Important Reminders*

• f(g(x)) and g(f(x)) are not interchangeable because they don't always produce the same solution. 
• The open dot "o" and the multiplication dot "•" are different.