Page 14 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

x x – 1 3
(c) g(x) = + 1 (d) h(x) = (e) h(x) =
4 2x + 1 x – 1
Let y = g(x) Let y = h(x) Let y = h(x)
x y = x – 1 3
y = + 1 2x + 1 y = x – 1
4
x 2xy + y = x – 1
= y – 1 xy – y = 3
4 y + 1 = x – 2xy
x = 4(y – 1) y + 1 = x(1 – 2y) xy = 3 + y
3 + y
x = 4y – 4 y + 1 x =
x = y
3
Since g (y) = x, 1 – 2y x = + 1
–1
–1
g (y) = 4y – 4 Since h (y) = x, y
–1
y + 1 Since h (y) = x,
–1
–1
Substitute y with x, h (y) = 1 – 2y 3
–1
–1
g (x) = 4x – 4 Substitute y with x, h (y) = + 1
y
–1
∴ g : x → 4x – 4 x + 1 Substitute y with x,
–1
h (x) =
3
1 – 2x h (x) = + 1
–1
x + 1 x
–1
∴ h : x →
3
1 – 2x ∴ h : x → + 1
–1
x
21. Find the function f, g or h based on the given inverse function. PL 4
Cari fungsi f, g dan h berdasarkan fungsi songsang yang diberikan.
Example (a) f (x) = 3x – 4 (b) f (x) = x + 6
–1
–1
4 + x 5
–1
f (x) = Let y = f (x)
–1
2 Let y = f (x)
–1
y = 3x – 4
–1
Let y = f (x) 3x = y + 4 y = x + 6
4 + x y + 4 5
y = x = 5y = x + 6
2 3
2y = 4 + x Since f (y) = x, x = 5y – 6
x = 2y – 4 y + 4
f (y) = Since f(y) = x,
3
Since f (y) = x, f(y) = 5y – 6
f (y) = 2y – 4 Substitute y with x,
f (x) = x + 4 Substitute y with x,
Substitute y with x, 3 f(x) = 5x – 6
f (x) = 2x – 4 ∴ f : x → x + 4
3 ∴ f : x → 5x – 6
∴ f : x → 2x – 4
x – 7 x + 4 5
–1
–1
(c) g (x) = (d) g (x) = (e) h (x) = – 2
–1
3 x – 4 x
–1
–1
–1
Let y = g (x) Let y = g (x) Let y = h (x)
5
y = x – 7 y = x + 4 y = – 2
3 x – 4 x
3y = x – 7 xy – 4y = x + 4 5 = y + 2
x = 3y + 7 xy – x = 4y + 4 x 5
x = 4y + 4 x = y + 2
Since g(y) = x, y – 1
g(y) = 3y + 7 Since g(y) = x, Since h(y) = x,
5
4y + 4 h(y) =
g(y) = y + 2
Substitute y with x, y – 1
g(x) = 3x + 7 Substitute y with x,
Substitute y with x, 5
∴ g : x → 3x + 7 g(x) = 4x + 4 h(x) = x + 2
x – 1 5
4x + 4 ∴ h : x →
∴ g : x → x + 2
x – 1
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