Page 12 - Top Class Additional Mathematics Tg 4

Additional Mathematics Form 4 Chapter 1 Functions

1.3 Inverse Functions Textbook
Fungsi Songsang
pg. 20 – 29

SMART Notes

1. f 5. Horizontal line test can be used to test the existence
of inverse functions.
Ujian garis mengufuk boleh digunakan untuk menguji
x y kewujudan fungsi songsang.
f –1
y
y = f(x)
If f(x) = y, then the inverse function is f (y) = x. f has inverse function
–1
Jika f(x) = y, maka fungsi songsangnya ialah f (y) = x. f mempunyai fungsi
–1
2. Only one-to-one functions have inverse functions. songsang
Hanya fungsi satu kepada satu mempunyai fungsi songsang. 0 x
3. f and g are inverse functions of each other if and only if
fg(x) = x, x in domain of g and gf(x) = x, x in domain of f.
f dan g ialah fungsi songsang antara satu sama lain jika dan y
hanya jika fg(x) = x, x dalam domain g dan gf(x) = x, x dalam h does not have
domain f. inverse function
4. If f and g are inverse functions of each other, then y = h(x) h tidak mempunyai
Jika f dan g ialah fungsi songsang antara satu sama lain, maka x fungsi songsang
(a) domain of f = range of g and domain of g = range of f 0
domain f = julat g dan domain g = julat f
(b) graph g is the reflection of graph f on the line y = x 7. ff (x) = f f(x) = x
–1
–1
graf g adalah pantulan graf f pada garis y = x

16. In the diagram, function f maps x to y. Determine each of the following. PL 1
Dalam rajah di bawah, fungsi f memetakan x kepada y. Tentukan setiap yang berikut.

f
–1
x y (a) f(2) = 3 (b) f (11) = 6
2
3
5
6
9 (c) f (3) = 2 (d) f (9) = 5
–1
–1
11
17. Determine whether the following functions have the inverse functions using the horizontal line test. PL 2
Tentukan sama ada fungsi berikut mempunyai fungsi songsang atau tidak dengan menggunakan ujian garis mengufuk.
Example (a) y (b) y
y
f
f

f x x
–1 0 3 0
x
0 2

Has inverse function. When tested Does not have inverse Has inverse function. When
with a horizontal line, the line cuts function. When tested with a tested with a horizontal line,
the graph at one point. horizontal line, the line cuts the line cuts the graph at one
the graph at two points. point.

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