Page 8 - Praktis Hebat 2021 - Additional Mathematics F4

Additional Mathematics Form 4 Practice 1 Functions
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4. Two functions are defined by f : x → 4x and g : x → 3x – x + 20. PL4 Subtopic 1.2
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TEXTBOOK Dua fungsi ditakrifkan oleh f : x → 4x dan g : x → 3x – x + 20.
pg. 12 – 19
(a) Find the composite function fg(x) and gf(x). Is fg(x) equal to gf(x)?
Cari fungsi gubahan fg(x) dan gf(x). Adakah fg(x) sama dengan gf(x)? [4 marks / markah]
(b) Find the possible values of x to satisfy the equation f (x) = g(x).
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Cari nilai-nilai x yang mungkin untuk memuaskan persamaan f (x) = g(x). [3 marks / markah]
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1
5. The function g and h are defined by g: x → x – 1 , x ≠ 1 and h : x → 2x + 3 respectively. PL4 Subtopic 1.2

TEXTBOOK Fungsi g dan h masing-masing ditakrifkan oleh g : x → 1 , x ≠ 1 dan h : x → 2x + 3.

pg. 12 – 19 x – 1
(a) Find the expression for gh(x), hg(x) g (x) and h (x).
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2
Cari ungkapan bagi gh(x), hg(x) g (x) dan h (x). [8 marks / markah]
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2
(b) Find the value of x when gh(x) = hg(x) – 31 .
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31
Cari nilai x apabila gh(x) = hg(x) – 8 . [2 marks / markah]
6. Given that the inverse function g (x) = x – 4 . PL4 Subtopic 1.3
–1
TEXTBOOK Diberi fungsi songsang g (x) = x – 4 . 11
–1
pg. 20 – 29 11
(a) Find the function g(x).
Cari fungsi g(x). [2 marks / markah]
(b) Solve the following equations.
Selesaikan persamaan yang berikut.
(i) g(x) = g (x) (ii) g(x) = gg (x) [4 marks / markah]
–1
–1
kx – 9 mx + n
–1
7. Given that f : x → x + 4 , x ≠ –4 and f : x → 5 – x , x ≠ 5. PL4 Subtopic 1.3
TEXTBOOK
pg. 20 – 29 Diberi bahawa f : x → kx – 9 , x ≠ –4 dan f : x → mx + n , x ≠ 5.
–1
x + 4 5 – x
(a) Find the values of k, m and n.
Cari nilai k, m dan n. [3 marks / markah]
(b) Find the value of x when f(x) + 11 = f (x).
–1
2
Cari nilai x apabila f(x) + 11 = f (x). [2 marks / markah]
–1
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(c) Determine whether ff (x) = x. Hence, determine whether each equation given is true or false. Give
–1
your reason.
Tentukan sama ada ff (x) = x. Seterusnya, tentukan sama ada setiap persamaan yang diberikan
–1
adalah benar atau palsu. Berikan alasan anda.
(i) ff (–2) = –2 (ii) ff (3) = –3 [5 marks / markah]
–1
–1
8. Given that f : x → 3x – 7 and g : x → 10 – 9x. PL3 Subtopic 1.1 & 1.2
TEXTBOOK Diberi bahawa f : x → 3x – 7 dan g : x → 10 – 9x.
pg. 2 – 19
(a) Find / Cari
(i) f (–3) [2 marks / markah]
(ii) the value of m if f(m – 4) = 1 f(–3)
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nilai m jika f(m – 4) = 1 f(–3) [2 marks / markah]
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(iii) gf(x) [3 marks / markah]
(b) Hence, sketch the graph of y = |gf(x)| for –2 < x < 4. State the range of y.
Seterusnya, lakar graf y = |gf(x)| untuk –2 < x < 4. Nyatakan julat y. [3 marks / markah]

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