Page 10 - PBD Plus Matematik Tambahan T4 (EG)

Matematik Tambahan Tingkatan 4 Bab 1 Fungsi
SP 1.1.3 Menentukan imej suatu fungsi apabila objek diberi dan sebaliknya.

5. Selesaikan setiap yang berikut. TP 3
Solve each of the following.
Contoh (a) Fungsi h ditakrifkan oleh h : x → x + 3x + 2. Cari
2
Fungsi f ditakrifkan oleh f : x → 2x + 6 . Cari Function h is defined by h : x → x + 3x + 2. Find
2
1
2x + 6 3 (i) h(–3) dan / and h   ,
Function f is defined by f : x → 3 . Find 2
3
(i) f(3) dan / and f   , (ii) nilai-nilai x yang mungkin jika imejnya ialah
2
30.
(ii) nilai x jika imejnya ialah 10. the possible values of x if the image is 30.
the value of x if the image is 10.
2
3
2   + 6 (i) h(–3) = (–3) + 3(–3) + 2
2(3) + 6 3 2 = 2
(i) f(3) = f   = 2
1
1
1
3 2 3 h     + 3   + 2
=
= 4 = 3 2 2 2
(ii) f(x) = 10 = 15
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2x + 6 = 10 4
3 (ii) x + 3x + 2 = 30
2
2x + 6 = 30 x + 3x – 28 = 0
2
2x = 24 (x – 4)(x + 7) = 0
x = 12 x = 4, –7
(b) Fungsi p ditakrifkan oleh p : x → kx + c. Diberi bahawa p(2) = 7 dan p(4) = –1, cari
Function p is defined by p : x → kx + c. Given that p(2) = 7 and p(4) = –1, find
(i) nilai k dan nilai c, (ii) imej bagi 3 di bawah p.
the value of k and of c, the image of 3 under p.
p(2) = 7 p(x) = –4x + 15
2k + c = 7......................a p(3) = –4(3) + 15
p(4) = –1 = 3
4k + c = –1....................b

a – b –2k = 8
k = –4
2(–4) + c = 7
c = 15

6. Selesaikan setiap yang berikut. TP 3
Solve each of the following.
Contoh
Fungsi f ditakrifkan oleh f : x → |x − 1|.
Function f is defined by f : x → |x − 1|.
(i) Lakarkan graf bagi f untuk domain −2  x  3. (iii) Cari domain bagi f(x)  2.
Sketch the graph of f in the domain −2  x  3. Find the domain of f(x)  2.
(ii) Cari nilai bagi f(–5). (iv) Cari domain bagi f(x)  4.
Find the value of f(–5). Find the domain of f(x)  4.
(i) x –2 0 1 3 (ii) f(–5) = |–5 – 1|
y = f(x) = |x – 1| 3 1 0 2 = |–6|
= 6
f(x)
(iii) f(x)  2
3 x – 1  –2 , x – 1  2
x  –1 x  3
2
(iv) f(x)  4
1 |x – 1|  4
–4  x – 1  4
x
0
–2 1 3 –3  x  5
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