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Unformatted text preview: and sometimes they won’t. © 2007 Paul Dawkins 189 http://tutorial.math.lamar.edu/terms.aspx College Algebra Combining Functions
The topic with functions that we need to deal with is combining functions. For the most part this
means performing basic arithmetic (addition, subtraction, multiplication, and division) with
functions. There is one new way of combing functions that we’ll need to look at as well.
Let’s start with basic arithmetic of functions. Given two functions f ( x ) and g ( x ) we have the
following notation and operations. ( f + g )( x) = f ( x) + g ( x) ( f - g )( x) = f ( x) - g ( x)
f ( x)
ç ÷( x) =
g ( x)
ègø ( fg )( x ) = f ( x ) g ( x ) Sometimes we will drop the ( x ) part and just write the following, f + g = f ( x) + g ( x) f - g = f ( x) - g ( x) fg = f ( x ) g ( x ) f ( x)
g g ( x) Note as well that we put x’s in the parenthesis, but we will often put in numbers as well. Let’s
take a quick look at an example. Example 1 Given f ( x ) = 2 + 3 x - x 2 and g ( x ) = 2 x - 1 evaluate each of the following.
(a) ( f + g ) ( 4) (b) g - f
(c) [Solution] [Solution] ( fg ) ( x ) [Solution] æfö
÷ ( 0 ) [Solution]
ègø (d) ç Soluti...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12