Algebra of Functions

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. ( fg)( x
  3. ( f × g)( x

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