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