Diketahui f(x) = ax + b; a > 0; dan f2(x) = (f o f)(x) = 4x - 9, nilai a2 + b2 =
Diketahui f(x) = ax + b; a > 0; dan f2(x) = (f o f)(x) = 4x - 9, nilai a2 + b2 = ….
Jawab:
f(x) = ax + b; a > 0; dan f2(x) = (f o f)(x) = 4x – 9
(f o f)(x) = 4x – 9
⇔ f(f(x)) = 4x – 9
⇔ f(ax + b) = 4x – 9
⇔ a(ax + b) + b = 4x – 9
⇔ a2x + ab + b = 4x – 9
maka a2 = 4 → a = ±2 → a = 2 (memenuhi a > 0)
ab + b = -9
⇔ 2b + b = -9
⇔ 3b = -9
⇔ b = -3
Jadi nilai a2 + b2 = 4 + (-3)2 = 4 + 9 = 13
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