Page 12 - Modul A+1 Matematik Tambahan Tingkatan 4

3. Fungsi f ditakrifkan oleh f : x → 5 – x. Cari fungsi g jika 5. Fungsi q ditakrifkan oleh q : x → 5 – x . Cari fungsi p jika
fg : x → 5x + 1. 2
2
Function f is defined by f : x → 5 – x. Find the function g if pq : x → x – 3.
fg : x → 5x + 1. Function q is defined by q : x → 5 – x . Find the function p if BAB 1
2
2
pq : x → x – 3.
f [g(x)] = 5x + 1
2
5 – g(x) = 5x + 1 p[q(x)] = x – 3
2
– g(x) = 5x + 1 – 5 5 – x
2
g(x) = –5x + 4 p  2  = x – 3
2
4. Diberi f (x) = 5x – 9 dan fg(x) = 2x + 3. Katakan 5 – x = y
2
Cari fungsi g(x). 2
Given f (x) = 5x – 9 and fg(x) = 2x + 3. 5 – x = 2y
2
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Find the function g(x). x = 5 – 2y
∴ p(y) = (5 – 2y) – 3
fg(x) = 2x + 3 = 2 – 2y
2
5g(x) – 9 = 2x + 3 Maka, p(x) = 2 – 2x
2
5g(x) = 2x + 3 + 9
2
2
g(x) = 2x + 12
5
6. Diberi k(x) = mx – n dan k (x) = 27x + 12. Cari nilai m 7. Diberi u(x) = 5 , x ≠ 7 dan vu(x) = 3 + x.
3
dan nilai n. 7 – x
Given k(x) = mx – n and k (x) = 27x + 12. Find the values of Cari fungsi v.
3
m and n. KBAT Menganalisis Given u(x) = 5 , x ≠ 7 and vu(x) = 3 + x.
7 – x
k[k(x)] = m(mx – n) – n = m x – mn – n Find the function v.
2
k (x) = k k(x) = m (mx – n) – mn – n
2
2
3
k (x) = m x – m n – mn – n vu(x) = 3 + x
2
3
3
Bandingkan dengan k (x) = 27x + 12 v  5  = 3 + x
3
m = 27 7 – x
3
m = 3 5
–m n – mn – n = 12 Katakan 7 – x = y
2
–3 n – 3n – n = 12 5 = 7y – xy
2
–9n – 3n – n = 12 xy = 7y – 5
n = – 12 x = 7y – 5
13 y
v(y) = 3 + 7y – 5
y
3y + 7y – 5
= y
10y – 5
= y
10x – 5
v(x) = x
x x
8. Suatu fungsi m ditakrifkan oleh m(x) = 1 – x . Tunjukkan bahawa m (x) = 1 – 3x . Seterusnya, cadangkan ungkapan yang
3
n
sesuai bagi m (x).
Function m is defined by m(x) = x . Show that m (x) = x . Hence, suggest a suitable expression for m (x). KBAT Menilai
3
n
1 – x 1 – 3x
x x
m (x) = 1 – x x m (x) = 1 – x
2
3
1 – 1 – 2  x 
1 – x 1 – x
x x x 2x


= 1 – x ÷ 1 – 1 – x  = 1 – x ÷ 1 – 1 – x 
x 1 – x x x 1 – x 2x
= 1 – x ÷  1 – x – 1 – x  = 1 – x ÷  1 – x – 1 – x 
x 1 – x x 1 – x
= 1 – x ×  1 – 2x  = 1 – x ×  1 – 3x 
x x
= 1 – 2x = 1 – 3x
m (x) = x
n
1 – nx
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