Page 13 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

18. Verify that f and g are inverse functions of each other. PL 3
Sahkan f dan g ialah fungsi songsang antara satu sama lain.
Example (a) f(x) = 4 – 3x, g(x) = 4 – x

f(x) = x – 8, g(x) = x + 8 3

fg(x) = f(x + 8) gf(x) = g(x – 8) 4 – x gf(x) = g(4 – 3x)
= (x + 8) – 8 = (x – 8) + 8 fg(x) = f  3 
= x = x 4 – x = 4 – (4 – 3x)
= 4 – 3  3  3
Since fg(x) = gf(x) = x, f and g are inverse functions = 4 – (4 – x) = 3x
3
of each other. = x = x

Since fg(x) = gf(x) = x, f and g are inverse
functions of each other.

–1
–1
19. Sketch graphs of f and f on the same plane. Then, state the domain of f . PL 3
Lakar graf bagi f dan f pada satah yang sama. Seterusnya, nyatakan domain bagi f .
–1
–1
Example (a) f : x → – , domain: 1 < x < 10
5
f : x → 4x, domain: 0 < x < 3 x
x 1 5 10
x 0 1 2 3
y –5 –1 –0.5
y 0 4 8 12
y
y (–0.5, 10)
(3, 12) y = x y = x
Domain of f :
–1
f –1 –5 < x < –0.5
–1
f Domain of f :
0 < x < 12 (–5, 1)
(12, 3) x
f –1 Range of f 0 f (10, –0.5)
x
0
(1, –5)

20. Find the inverse function of each of the following functions. PL 3
Cari fungsi songsang bagi setiap fungsi berikut.
Example (a) f(x) = 3x – 1 (b) g(x) = 7 – 2x

f(x) = 4x + 5
Let y = f(x) Let y = g(x)
y = 3x – 1 y = 7 – 2x
Let y = f(x) 3x = y + 1 2x = 7 – y
y = 4x + 5 y + 1 7 – y
4x = y – 5 x = 3 x = 2
y – 5
x = –1 –1
4 Since f (y) = x, Since g (y) = x,
–1
–1
f (y) = y + 1 g (y) = 7 – y
Since f (y) = x, 3 2
–1
y – 5
f (y) =
–1
4 Substitute y with x, Substitute y with x,
f (x) = x + 1 g (x) = 7 – x
–1
–1
Substitute y with x, 3 2
x – 5 x + 1 7 – x
–1
–1
f (x) = ∴ f : x → ∴ g : x →
–1
4 3 2
x – 5
∴ f : x →
–1
4
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