Precalculus Name: 1.4 Function Composition Period: PART 1: COMBINING FUNCTIONS GRAPHICALLY & NUMERICALLY

( ) 2f x x ( ) 4g x x

The Algebraic rule for f(x) + g(x)

( ) ( ) 2 ( 4)f x g x x x

BIG IDEA!

The domain of the sum of two functions is:

Make a prediction! Domain of the difference of two functions:

x f(x)

-1

0

2

4.5

8

12.5

x g(x)

-1

0

2

4.5

8

12.5

Domain of f(x): Domain of g(x):

x f(x)+g(x)

-1

0

2

4.5

8

12.5

Domain of f(x)+ g(x):

PART 2: FUNCTION COMPOSITION

Composition f of g: ( )( )f g x

Composition g of f: ( )( )g f x

But what does it mean??

A few for practice …

1. If ( ) 2f x x and ( ) 4g x x ... evaluate:

a. ( ( ))f g x

b. ( ( ))g f x

2. If ( ) 3k x x and 2( )w x x …. evaluate:

a. ( )( )k w x

b. ( )( )w k x

Pick it up! Finding the domain of a composed function.

1. Compose the functions without simplifying the result. 2. Find the domain of the UNSIMPLIFIED composition as we have found domains in the past.

Give it a shot!

If 2( ) 1f x x and ( )g x x ….

FIRST! Evaluate:

a. ( ( ))f g x

b. ( ( ))g f x

THEN! Find the domain of:

a. ( ( ))f g x b. ( ( ))g f x