Page 19 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions
3. (a) Given the functions f : x → 3x – 4 and g : x → 2 – 5x, 4. Given f : x → x + 3 and g : x → 4 , x ≠ 2, find
SPM find 7 x – 2
2018 x + 3 4
Diberi fungsi f : x → 3x – 4 dan g : x → 2 – 5x, cari Diberi f : x → dan g : x → , x ≠ 2, cari
(i) g(4), (a) g (x), 7 x – 2
–1
1
(ii) the value of n if f (n + 1) = g(4), [2]
6
1
–1
nilai n jika f(n + 1) = g(4), (b) g f(x), [2]
6
(iii) gf(x). (c) the value of x if (f ) (x) = 25.
–1 2
[5] –1 2
(b) Hence, sketch the graph of y = gf(x) for –1 < x < 3. nilai x jika (f ) (x) = 25.
State the range of y. [3]
Seterusnya, lakar graf y = gf(x) untuk –1 < x < 3. Ans: (a) g (x) = 4 x + 2, x ≠ 0
–1
Nyatakan julat bagi y.
[3] (b) g f(x) = 34 + 2x , x ≠ –3
–1
2 x + 3
Ans: (a) (i) –18; (ii) n = – 3 ; (iii) gf(x) = 22 – 15x (c) x = 1
(b) Range: 0 < y < 37
HOTS Challenge

1. Money in Malaysian Ringgit (RM) is converted to Indonesian Rupiah (Rp) according to the function f(x) = 3 388.50x, where
f(x) is money in Indonesian Rupiah (Rp) and x is money in Malaysian Ringgit (RM). HOTS Analysing
Wang dalam Ringgit Malaysia (RM) ditukar kepada Rupiah Indonesia (Rp) menurut fungsi f(x) = 3 388.50x, dengan keadaan f(x)
ialah wang dalam Rupiah Indonesia (Rp) dan x ialah wang dalam Ringgit Malaysia (RM).
(a) How much money is there in Indonesian Rupiah (Rp) if the money in Malaysian Ringgit (RM) is RM800?
Berapakah jumlah wang dalam Rupiah Indonesia (Rp) jika wang dalam Ringgit Malaysia (RM) ialah RM800?
(b) Find the inverse function of the function f(x). What is the meaning of the inverse function obtained?
Cari fungsi songsang bagi fungsi f(x) ini. Apakah maksud fungsi songsang yang diperoleh?
Answer Guide
Apply concepts in functions and inverse functions.
Gunakan konsep dalam fungsi dan fungsi songsang.

Ans: (a) 2 710 800 Rp
x
(b) f (x) = ; The inverse function obtained converts money in Indonesian Rupiah (Rp) to Malaysian
–1
3 388.50
Ringgit (RM).
mx 9x – 15
2. Given f : x → , x ≠ n, g : x → 2x – m and the composite function gf : x → , find HOTS Applying
n – x 5 – x
Diberi f : x → mx , x ≠ n, g : x → 2x – m dan fungsi gubahan gf : x → 9x – 15 , cari
n – x 5 – x
(a) the values of m and n, (b) the inverse functions of f and g, (c) the values of x if g = fg.
nilai m dan n, fungsi songsang bagi f dan g, nilai x jika g = fg.
Answer Guide
Apply concepts in composite functions and inverse functions.
Gunakan konsep dalam fungsi gubahan dan fungsi songsang.

Ans: (a) m = 3, n = 5
5x x + 3
–1
(b) f (x) = , g (x) =
–1
3 + x 2
5 3
(c) x = or
2 2

Quiz 1
21
PAK-

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