Jika f fungsi dari himpunan bilangan asli ke himpunan bilangan asli yang memenuhi f(x) + f(x+1)= 2x² dan f(31) = 99, maka f(99)=..... A. 8.673 B. 8.772 C. 8.871 D. 9.505 E. 9.604

Jawaban: C. 8.871 perhatikan konsep fungsi berikut: misal f(x) = ax^2 jika x = c, maka: f(c) = a(c)^2 Diketahui: f(x) + f(x + 1) = 2x^2 f(31) = 99 DItanya: f(99) = ...? Pembahasan: f(x) + f(x + 1) = 2x^2 f(x + 1) = 2x^2 - f(x) misal x = 98 f(98 + 1) = 2(98)^2 - f(98) f(99) = 2(98)^2 - f(98) f(x + 1) = 2x^2 - f(x) misal x = 97 f(97 + 1) = 2(97)^2 - f(97) f(98) = 2(97)^2 - f(97) f(x + 1) = 2x^2 - f(x) misal x = 96 f(96 + 1) = 2(96)^2 - f(96) f(97) = 2(96)^2 - f(96) f(x + 1) = 2x^2 - f(x) misal x = 30 f(30 + 1) = 2(30)^2 - f(30) f(31) = 2(30)^2 - f(30) dan seterusnya... Maka: f(99) = 2(98)^2 - [f(98)] f(99) = 2(98)^2 - [2(97)^2 - f(97)] f(99) = 2(98)^2 - 2(97)^2 + [f(97)] f(99) = 2(98)^2 - 2(97)^2 + [2(96)^2 - f(96)] f(99) = 2(98)^2 - 2(97)^2 + 2(96)^2 - [f(96)] f(99) = 2(98)^2 - 2(97)^2 + 2(96)^2 - [2(95)^2 - f(95)] dst.... maka: f(99) = 2(98)^2 - 2(97)^2 + 2(96)^2 - [2(95)^2 - f(95)] f(99) = 2(98)^2 - 2(97)^2 + 2(96)^2 - 2(95)^2 + ... - 2(31)^2 + f(31) f(99) = 2 ((98)^2 - (97)^2 + (96)^2 - (95)^2) + ... - (31)^2) + f(31) f(99) = 2 ((98)(98) - (97)(97) + (96)(96) - (95)(95)) + ... - (31)(31)) + f(31) f(99) = 2 ((98 - 97)(98 + 97) + (97 - 96)(96 + 95) + ... + (32 - 31)(32 + 31)) + 99 f(99) = 2 (98 + 97 + 96 + ... + 63) + 99 f(99) = (9702 - 630) + 99 f(99) = 8.871 Jadi, nilai dari f(99) = 8.871 pilihan jawaban yang tepat = C.