Jawaban Soal Ujian Matematika Ipa Kelas 12 No 6 Tahun 2017

Soal Ujian Matematika IPA Kelas 12

Tahun 2017

Soal Pilihan Ganda

6. Jika fungsi f(x) = (2x + 3) / (x - 5) , x ≠ -5 dan g(x) = 3x + 1, maka (g o f)^-1(x) = ...

A. (5x + 4) / (x + 7) , x ≠ - 7
B. (5x + 7) / (x - 4) , x ≠ 4
C. (5x + 4) / (x - 7) , x ≠ 7
D. (5x - 4) / (x - 7) , x ≠ 7
E. (5x - 7) / (x - 4) , x ≠ 4

Jawaban : C

g(x) = 3x + 1
f(x) = (2x + 3) / (x - 5)

(g o f)(x) ?
g (f (x)) = 3((2x + 3) / (x - 5)) + 1
g (f (x)) = (6x + 9) / (x - 5)) + 1
g (f (x)) = (6x + 9) / (x - 5)) + (x - 5)/(x - 5)
g (f (x)) = (6x + 9 + x - 5) / (x - 5)
g (f (x)) = (7x + 4) / (x - 5)

(g o f)^-1(x) ?
misalkan g (f (x)) = y
y = (7x + 4) / (x - 5)
y (x - 5) = 7x + 4
yx - 5y = 7x + 4
- 7x + yx = 4 + 5y
x (y - 7) = 5y + 4
x = (5y + 4) / (y - 7)

sehingga :
(g o f)^-1(x) = (5x + 4) / (x - 7)

>>>Soal No.7