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
= (1/2).(2/3).(3/4)....(98/99).(99/100)
= 1/100
Mapel: Matematika
Kelas: 10
Materi: Komposisi Fungsi
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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