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Unformatted text preview: the last example from the previous section we looked at the two functions f ( x ) = 3 x - 2 and g ( x) = x2
+ and saw that
33 ( f o g )( x) = ( g o f ) ( x) = x and as noted in that section this means that these are very special functions. Let’s see just what
makes them so special. Consider the following evaluations. -5 2 -3
333 f ( -1) = 3 ( -1) - 2 = -5 Þ g ( -5 ) = 224
333 Þ 4ö
f ç ÷ = 3ç ÷ - 2 = 4 - 2 = 2
è3ø g ( 2) = In the first case we plugged x = -1 into f ( x ) and got a value of -5. We then turned around and
plugged x = -5 into g ( x ) and got a value of -1, the number that we started off with.
In the second case we did something similar. Here we plugged x = 2 into g ( x ) and got a value
, we turned around and plugged this into f ( x ) and got a value of 2, which is again the
3 number that we started with.
Note that we really are doing some function composition here. The first case is really, ( g o f ) ( -1) = g é f ( -1) ù = g [ -5] = -1
û and the second case is really, ( f o g )( 2 ) = é4ù
f é g ( 2)ù = f ê ú = 2
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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