Question

Diketahui f (x) = 1+1/x,x≠0 dan (fog) (x) = 2x-1/x-1, x≠1. nilai (g(2)).!g(3)).(g(4))....(g(99)).(g(100))=​

Answer 1

Diketahui:

f(x) = 1+1/x

(fog) = (2x-1)/(x-1)

Ditanyakan:

g(2).g(3).g(4).....g(99).g(100)

Jawab:

(fog)(x) = f(g(x))

(2x-1)/(x-1) = 1+1/g(x)

(2x-1)/(x-1) -1 = 1/g(x)

(2x-1)/(x-1) - (x-1)/(x-1) = 1/g(x)

((2x-1)-(x-1))/(x-1) = 1/g(x)

(2x-1-x+1)/(x-1) = 1/g(x)

x/(x-1) = 1/g(x)

g(x) = (x-1)/x

g(2) = (2-1)/2 = 1/2

g(3) = (3-1)/3 = 2/3

g(4) = (4-1)/4 = 3/4

g(2).g(3).g(4).....g(99).g(100)

= (1/2).(2/3).(3/4)....(98/99).(99/100)

= 1/100

Mapel: Matematika

Kelas: 10

Materi: Komposisi Fungsi