Algebra of Functions

ReviewFunction notation: f(x)This DOES NOT MEAN MULITPLICATION.Given f(x) = 3x - 1, find f(2).Substitute 2 for xf(2) = 3(2) - 1 = 6 - 1 = 5

Given f(x) = x - 5, find f(a+1)

f(a + 1) = (a + 1) - 5 = a+1 - 5

f(a + 1) = a - 4

Review

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Objectives

To define the sum, difference, product, and quotient of functions.

To form and evaluate composite functions.

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Basic function operationsSum

Difference

Product

Quotient , 0

f xff g x x g x

g g x

f g x f x g x+ +

– –f g x f x g x

f g x f x g x

Function operations If and

find:

2

1)(

x

xxf xxg 4)(

2

174

2

)2(41

42

1

2

x

xx

x

xxx

xx

x

gf

Function operations If and

find:

2

1)(

x

xxf xxg 4)(

2

194

2

)2(41

42

1

2

x

xx

x

xxx

xx

x

gf

Function operations If and

find:

2

1)(

x

xxf xxg 4)(

2

44

1

4

2

1

42

1

2

x

xx

x

x

x

xx

x

gf

Function operations If and

find:

2

1)(

x

xxf xxg 4)(

xx

xxx

x

xx

x

gf

84

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1

2

1

42

1

/

2

Function Composition

Function Composition is just fancy substitution, very similar to what we have been doing with finding the value of a function.

The difference is we will be plugging in another function

Function CompositionJust the same we will still be replacing x with

whatever we have in the parentheses.The notation looks like We read it ‘f of g of x’

)(xgf

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Composition of functionsComposition of functions is the successive

application of the functions in a specific order.

Given two functions f and g, the composite function is defined by and is read “f of g of x.”f g f g x f g x

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g x

A different way to look at it…

FunctionMachine

x f g x

FunctionMachine

gf

Let’s watch the other PowerPoint for examples

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