Tentukan :
a. nilai a jika (f o g o h)(1)=8 dan
b. rumus fungsi (h o g o f)(x)
Diketahui f(x)=x²-x+8,g(x)=x/3,dan h(x)=2x+a dengaan a>0.
Jawaban Terkonfirmasi
Jawab
(fogoh)(1) = 8
fo (goh(1)) = 8
f o g (2+a) =8
f ((2+a)/3) =8
((2+a)/3)² – (2+ a)/3 + 8 = 8
(2+a)²/9 – (2 + a)/3 + 8 = 8
(2+a)²/9 – (2+a)/3 = 0
(2+a)² – 3(2+a) = 0
(2+a)(2+a – 3) = 0
(2+a)(a- 1)= 0
a = -2 atau a = 1
b. rumus (hogof)x =
= ho{ gof(x)}
= ho {g(x² – x +8)}
= ho {(x² -x + 8)/3}
= 2(x² -x +8)/3
= 2/3(x² – x + 8)