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The Algebra of Functions
Given two functions, f(x) and g(x), we use shorthand notation to indicate the operations
of adding, subtracting, multiplying, and dividing the formulas of these two functions.
Furthermore, we have shorthand notation to indicate that the entire formula of one
function is inputted into the other function.
These operations, known as Algebra of
Functions, are described below.
Notation For Adding, Subtracting, Multiplying, and Dividing Functions:
(f + g)(x) = f(x) + g(x)
Example:
If f(x) = 3x + 2
and g(x) = x
2
, then (f + g)(x) = 3x + 2 + x
2
So, you simply add the two formulas together.
(f  g)(x) = f(x)  g(x)
Example:
If f(x) = 3x + 2
and g(x) = x
2
, then (f + g)(x) = 3x + 2  x
2
So, you simply subtract the formulas.
(f
g)(x) = f(x)
•
g(x)
Example:
If f(x) = 3x + 2
and g(x) = x
2
, then (f + g)(x) = (3x + 2)
•
x
2
So, you simply multiply the two formulas together.
(f / g)(x) = f(x) / g(x),
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This note was uploaded on 11/05/2011 for the course ANTHRO 101 taught by Professor Crandall during the Fall '09 term at BYU.
 Fall '09
 Crandall
 Anthropology

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