section 2.7 combining functions objectives: to add, subtract, multiply and divide functions....
Post on 20-Jan-2018
212 Views
Preview:
DESCRIPTION
TRANSCRIPT
Section 2.7Combining Functions
Objectives:•To add, subtract, multiply and divide functions.•Composition of functions.
Two functions f and g can be combined to form new functions
f + g, f – g, fg, f/g
in a manner similar to the way we add, subtract, multiply, and divide real numbers.
( )( ) ( ) ( ) Domain ( )( ) ( ) ( ) Domain
( )( ) ( ) ( ) Domain
( )( ) Domain { | ( ) 0}( )
f g x f x g x A Bf g x f x g x A B
fg x f x g x A B
f f xx x A B g xg g x
Let f and g be functions with domains A and B.Then, the functions f + g, f – g, fg, and f/g
are defined as follows.
Ex 1. Let and
(a) Find the functions f + g, f – g, fg, and f/g and their domains.
(b) Find (f + g)(-1), (f – g)(3), (fg)(4), and (f/g)(2).
2( ) 4f x x x 2( ) 6g x x
Class Work
1. Let and
a.) Find the function and its domain.
b.) Find
2( )f x x ( ) 2g x x
f g
( )(8)f g
• Given two functions f and g, the composite function f ◦ g (also called the composition of f and g) is defined by:
(f ◦ g)(x) = f [g(x)]
Ex 2. Let f(x) = x2 and g(x) = x – 3
(a) Find the functions f ◦ g and g ◦ f and their domains.
(b) Find (f ◦ g)(5) and (g ◦ f )(7).
Class Work
2. Let f(x) = x2 and g(x) = x + 5.
(a) Find the functions f ◦ g and g ◦ f and their domains.
(b) Find (f ◦ g)(-2) and (g ◦ f )(4).
Ex 3.
If f(x) = and g(x) = , find the following functions and their domains.
(a) f ◦ g(b) g ◦ f(c) f ◦ f(d) g ◦ g
x 2 x
Class Work
3. Let . Find:a)
b)
c)
10, ( ) , ( ) 31xf x g x x h x xx
f g
g h
f h
HW #7 p219 1-9odd, 17-21 odd, 23-35 odd
top related