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.

( f + g)( x)

( f – g)( x)

( f × g)( x)


The common domain is {all real numbers}.

The common domain is {all real numbers}.

( f × g)( x) = ( x + 4) × ( x ^{2} – 2 x – 3)
Use the distributive property.
The common domain is {all real numbers}.

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