Name:
Date:
Instructor:
Notes for 2.7 Operations on Functions, Composition of
Functions (pp. 268 - 275)
Topics: Add, Subtract, Multiply, Divide and Compose Two
Functions
I. Arithmetic Operations of Functions(pp. 268 – 270)
Given two functions f and g, then for all values of x for which both f(x) and g(x) are defined as:
A. (f + g)(x) = _______________________ (*Combine similar terms.)
B. (f – g)(x) = _______________________ (*Distribute the negative 1 through the second
function, then combine similar terms.)
C. (fg)(x) = _____________________(*Multiply the two functions together using FOIL,
distributive property or just writing them side-by-side, as on the video)
D. ( ) ________________
fx
g
=
(*Write as a single fraction and reduce when appropriate.
Exclude all values that would make the denominator become 0 when substituted in for x.)
*Omit problems concerning the domain of the result. This is not tested in this course. Sorry that
it’s scattered throughout the video.
*Always write out the operation’s definition above as the first step of the solution, then evaluate
at a number or clean up as outlined above.
Ex. 2
() 4fx x=− and ()gx x=
a. (f + g)(9) =
b. (f + g)(x) =
c. (f – g)(0) =
d. (f – g)(x) =
e. (fg)(1) =
f. (fg)(x) =
g. (4)
f
g
=
h. ()
f
x
g
=
