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Unformatted text preview: ferent answers depending on the order we’ve listed them.
Finally, function composition is really nothing more than function evaluation. All we’re really
doing is plugging the second function listed into the first function listed. In the definitions we
used [ ] for the function evaluation instead of the standard ( ) to avoid confusion with too
many sets of parenthesis, but the evaluation will work the same.
Let’s take a look at a couple of examples. Example 2 Given f ( x ) = 2 + 3 x  x 2 and g ( x ) = 2 x  1 evaluate each of the following. ( fg ) ( x ) [Solution]
(b) ( f o g ) ( x ) [Solution]
(c) ( g o f ) ( x ) [Solution]
(a) Solution
(a) These are the same functions that we used in the first set of examples and we’ve already done
this part there so we won’t redo all the work here. It is here only here to prove the point that
function composition is NOT function multiplication.
Here is the multiplication of these two functions. ( fg ) ( x ) = 2 x3 + 7 x 2 + x  2
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 Spring '12
 MrVinh

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