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Form Five                                                            Form Five


          Answers to Exercise 4.6                          x −  2  3x +  2    1   1
                                                    fx
                                  ( ( ))x = −
                                                 1. Not commutative.
          1.  f  ( ( ))gx = − 3x + 17,  gf  3x −  (a) ( ) =  2 x     , f     =  2
                                                               −
                                                                          2 
                                                                         
                        x −  2  3x +  2    1   1                   1   7
          2.  (a) ( ) =           , f     =   (b) ( ) =  fx  3x +  2, f     =
                 fx
         FOR ONLINE READING ONLY
                          2 x           2   2                      2   2
                            −
                                         }
                                       7
          3.  (g f fx )( )x = {( 1,−   1), 1  (0, 5)   Domain = { : 1,0x −  } ,
                                     =
                        3x +
                            2, f
             (b) ( ) =
                                  
                                  2   2   Range { :1, 5}y=
                                                              3
                                                              x
          4.  (a) ( f g  )()x =  x +  2  6x +  7     (c) ( f g  )()x = e − 2
                             2
             (b) ( f g  )()x =  x − 7        (d) ( f g  )( ) x =  x
               7
          6.  −                7.  x =± 5
          8.   (a) 34          (b) 112            (c) 584       (d) 130
              (e) 2706         (f)  x −  2x + 3
                                    2
          9.  (a)  32x −  2  312x +  685               (b)  512x −  3  4576x +  10149
          10. (a)  f g =  {(7, 5), ( 5, 8)}−   and  g f =  {(3, 10), (2, 7),(4, 3)}
          11.   g f =  {( 2, 1), (0,3)}−       12.  f g =  {(2,6), (4, 7)}
          Graphs of composite functions
          Teaching steps
             1.  Assist students through discussion to realize that, the procedures
                 for drawing graphs of composite functions are similar to those
                 of other functions.
             2.  Use Examples 4.25 and 4.26 in the Student’s Book to guide
                 students to sketch graphs of composite  functions. Engage
                 students to use GeoGebra or any other mathematical software
                 to verify the answers for the given examples. Advise them to
                 share their findings for more inputs.
             3.  Instruct students to attempt Exercise 4.7 in the Student’s Book.
                 Advise students to submit their work, check the correctness of
                 the answers, and provide them constructive feedback.


                                   65
                                             Mathematics for Advanced Secondary Schools



   ADVANCED MATH F.5 TG CHAPTERS.indd   65                              30/06/2024   18:02:05
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