SECTION 1.5: COMBINATIONS

OF FUNCTIONS

TARGET 1C: EVALUATE AND PERFORM OPERATIONS WITH FUNCTION NOTATION.

Combinations of Functions:

Just as with two real numbers where we can use operations such as addition, subtraction, multiplication and division; we can do the same with functions.

EX 1: Given f and .

Find f (7)

 

Find g (7)

 

Find f (7) – g (7)

Find (f – g)(x)

Find (f - g)(7)

Let f and g be distinct functions, then:

( )

( )

( )

( )

f g x

f g x

fg x

fx

g

EX 2: Let and ( ) 2 1f x x 2( ) 2 1.g x x x

a. Find and then evaluate at x = 2( )( )f g x

b. Find and then evaluate at x = 2( )( )f g x

EX 3: Let and 2( )f x x ( ) 3.g x x

a. Find and then evaluate at x = 4( )( )f g x

b. Find and state the domain.( )f

xg

EX 4: Let and 2( ) 3f x x ( ) 5.g x x

Find , , and .

Then evaluate all the composite functions at x = 3 and

state the domain for .

( )( )f g x ( )( )f g x ( )( )f g x ( )f

xg

( )f

xg