Here is the process finding the inverse of a function

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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 += = -1 333 f ( -1) = 3 ( -1) - 2 = -5 Þ g ( -5 ) = 224 += 333 Þ 4ö æ4ö f ç ÷ = 3ç ÷ - 2 = 4 - 2 = 2 è3ø 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 of 4 , 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 ë û and the second case is really, ( f o g )( 2 ) = é4ù f é g ( 2)ù = f ê ú = 2 ë û ë3...
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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.

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