Algebra of Functions

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

equation

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)

  4. equation

  5. equation

The common domain is {all real numbers}.

  1. equation

The common domain is {all real numbers}.

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

Use the distributive property.

equation

The common domain is {all real numbers}.

  1. equation

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