6.6 Function Operations
Function Operation
Addition (f+g)(x) = f(x) + g(x)
Multiplication (f * g)(x) = f(x) * g(x)
Subtraction (f-g)(x) = f(x) – g(x)
Division (f/g)(x) = f(x) / g(x) , g(x)≠0
Example:
Let f(x) = 5x2-4x and g(x) = 5x+1, find f+g
and f-g.
f+g = 5x2-4x + 5x+1
= 5x2+x+1
f-g = 5x2-4x –(5x+1)
= 5x2-9x-1
Example 2:
Let f(x) = 6x2+7x-5 and g(x) = 2x-1
Find f * g and f/g
f*g = (6x2+7x-5) * (2x-1)
= 12x3+8x2-17x+5
f/g = 6x2+7x-5 / (2x-1)
= (3x+5)(2x-1) / (2x-1)
= (3x+5) x≠1/2
Composition of Functions
The composition of function g with function f
is written as g ٥ f or (g ٥ f) (x) and is
defined as :
(g ٥ f) (x) = g ( f (x))
You evaluate the inner function first, then
use your answer as the input of the outer
function.
Example:
Let f(x) = x-2 and g(x) = x2 evaluate
(g ٥ f) (-5).
(g ٥ f) (-5) = g (f (-5)) = g ( -5-2)
= g(-7) = (-7)2 = 49
You Try: (f ٥ g) (-5)
Answer: 23
What is (f ٥ g) (x) in general?
f(g(x)) = f(x2) = x2 – 2
What about (g ٥ f) (x) = g ( f(x)) =
g( x – 2 ) = (x-2)2
= x2 – 4x + 4
Typically f(g(x)) doesn’t equal g(f(x))
HW pg 401 9 – 43 odd