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Section 4 - Combinations of Functions

Page history last edited by PBworks 14 years, 4 months ago

 

 

1.4 Combinations of Functuons

 

In this section you will be learning how to combine functions using Arithmetic Combinations of Functions, which are listed below.

 

Arithmetic Combinations of Functions

1. (f+ g)(x)= f(x)+g(x)

2. (f-g)(x)= f(x)-g(x)

3. (fg)(x)= f(x)*g(x)

4. (f/g)(x)= f(x)/g(x)

 

Ex. 1)Solve for all arithmetic combinations of functions when f(x)=2x+1 g(x)=x²+2x-1.

(f+g)(x)= 2x+1+x²+2x-1

(f+g)(x)= x²+4x

 

(f-g)(x)= 2x+1-(x²+2x-1)

(f-g)(x)= 2x+1-x²-2x+1

(f-g)(x)=-x²+2

 

(fg)(x)=(2x+1)(x²+2x-1)

(fg)(x)=2x³+4x²-2x+x²+2x-1

(fg)(x)=2x³+5x²-1

 

(f/g)(x)= eq=frac{2x+1}{x²+2x-1}

 

The composition of f with g: f(g(x)) or (feq=circg)(x)

-"eq=circ" is the equivalent to "of"

 

Ex. 2) Find f(g(x)) when f(x)=x+2 and g(x)=4-x².

f(g(x))=4-x²+2

f(g(x))=-x²+6

 

g(f(x))=4-(x+2)²

g(f(x))=4-(x²+4x+4)

g(f(x))=4-x²-4x-4

g(f(x))=-x²-4x

 

Ex. 3) Find f(x)+g(x)

f(g(x))=(3x-5)³

g(x)=3x-5

f(x)=x³

 

 

 

Comments (1)

Anonymous said

at 8:20 pm on Jan 8, 2008

Nice job, guys! 20/20

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