Function Operations and Composition Operations on Functions – Sum (f + g)(x) = f(x) + g(x)

Domain

Difference (f – g)(x) = f(x) – g(x)

Domain

Product (f ● g)(x) = f(x) ● g(x)

Domain

f  f ( x) Quotient   ( x) = g ( x) g Ex: f(x) = x 2 , g(x) = (f + g)(x) =

(f – g)(x) =

(f ● g)(x) =

 f    ( x) = g

Domain

x − 3 - Tell Domain and range of each of the following

Composite Functions: NOT MULTIPLICATION!!!!! Start on the inside and work your way back out f(g(x)) – f of g of x x

Domain of g

g(x)

Range of g

f(g(x))

Domain of f

Range of f(g(x))

Domain of f o g is the set of all x in the domain of g such that g(x) is in the domain of f. f o g(x) is defined whenever both g(x) and f(g(x)) are defined.

Ex: f ( x ) = x 2 , g ( x ) = x − 3 f(g(4)) =

( g
f ) (2) =

( f
f ) (−2) =

( g
g ) (−1) =

f ( g ( x )) =

find domain

g ( f ( x )) =

find domain