Diberikan fungsi g(x) = mx + n dan (g o g)(x) = 49x + 48
Diberikan fungsi g(x) = mx + n dan (g o g)(x) = 49x + 48.
a. Tentukan nilai m dan n.
b. Untuk m > 0, tentukan nilai x jika 4g(x) = g(2x - 3) - 3.
Jawab:
g(x) = mx + n
(g o g)(x) = 49x + 48
a. (g o g)(x) = g(mx + n)
⇔ 49x + 48 = m(mx + n) + n
⇔ 49x + 48 = m2x + nm + n
m2 = 49 → m = ±7
mn + n = 48 → 7n + n = 48 → 8n = 48 → n = 6
mn + n = 48 → -7n + n = 48 → -6n = 48 → n = -8
b. g(x) = 7x + 6
4g(x) = g(2x – 3) – 3
⇔ 4(7x + 6) = 7(2x – 3) + 6 – 3
⇔ 28x + 24 = 14x – 21 + 3
⇔ 28x – 14x = -18 - 24
⇔ 14x = -42
⇔ x = -3
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