Algebra II

If two functions have a common domain, then arithmetic can be performed with them using the following definitions.

Example 1

If f ( x) = x + 4 and g( x) = x ² – 2 x – 3, find each of the following and determine the common domain. 

1. ( f + g)( x) 
2. ( f – g)( x) 
3. ( f × g)( x) 
4. 
5. 

The common domain is {all real numbers}.

The common domain is {all real numbers}.

1. ( f × g)( x) = ( x + 4) × ( x ² – 2 x – 3) 

Use the distributive property.

The common domain is {all real numbers}.

1. 
2. This expression is undefined when x = 3 or when x = –1. So the common domain is {all real numbers except 3 or –1}.