6-6 Function Operations
 Find the sum, difference, product, and quotient.
Operations with functions: f(x)= x+1 g(x)= 6x
Sum
(f+g)(x) =f(x) + g(x)
(x+1)+6x=7x+1
Difference
(f-g)(x) =f(x) - g(x)
(x+1)-6x=-5x+1
Product
(f•g)(x) =f(x) • g(x)
(x+1)6x=6x2+6x
Quotient
(ex)
f(x)=x2-2x+1
g(x)=5x+1
Find (f+g)(x): ( x2-2x+1)+(5x+1)= x2+3x+2
Find (f-g)(x): ( x2-2x+1)-(5x+1)= ( x2-2x+1)+(-5x-1)= x2-7x
Remember to combine
like terms
Find (f•g)(x): ( x2-2x+1) (5x+1)=5x3-10x2+5x+x2-2x+1= 5x3-9x2+3x+1
Find
:
=
=
Remember the denominator can’t
equal zero.
nothing can reduce so the
original is your answer
(14) f(x) =7x+5 g(x) =
Find
Remember the denominator can’t
equal zero.
:
nothing can reduce so the
original is your answer
Find (g-f)(x): (
)-
Distribute the negative 1
(20) f(x) =2-x g(x) =
Find
Remember the denominator can’t
equal zero.
:
Remember we don't divide by
fraction by mult. by the reciprocal
Remember the denominator can’t
equal zero.
Compositions of functions:
plug g(x) answer into f(x) equation
plug f(x) answer into g(x) equation
f(x)=2x
g(x) =
(ex)
=
(ex)
=
f(x)=
g(x) =
(ex)
=
(ex)
=