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Unformatted text preview: unction multiplication.
[Return to Problems] (c) We’ll not put in the detail in this part as it works essentially the same as the previous part. ( g o f ) ( x ) = g é f ( x )ù
û = g é 2 + 3x - x 2 ù
û = 2 ( 2 + 3x - x 2 ) - 1
= 4 + 6 x - 2 x2 - 1
= -2 x 2 + 6 x + 3
Notice that this is NOT the same answer as that from the second part. In most cases the order in
which we do the function composition will give different answers.
[Return to Problems] The ideas from the previous example are important enough to make again. First, function
composition is NOT function multiplication. Second, the order in which we do function
composition is important. In most case we will get different answers with a different order. Note
however, that there are times when we will get the same answer regardless of the order.
Let’s work a couple more examples. Example 3 Given f ( x ) = x 2 - 3 and h ( x ) = x + 1 evaluate each of the following. ( f o h) ( x)
(b) ( h o f ) ( x )
(c) ( f o f ) ( x )
(d) ( h o h ) ( 8 )
(e) ( f o h ) ( 4...
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- Spring '12