Soal Un Matematika Ipa 2015 No 12

Soal UN Matematika IPA 2015

12. Diketahui f(x) = 3x - 5 dan g(x) = (4x + 7) / (2x + 3) , x ≠ - 3/2 , invers (f o g) (x) ialah ...

A. (f o g)^-1 (x) = (2x + 6) / (2x + 3) , x ≠ -3/2
B. (f o g)^-1 (x) = (3x + 6) / (2x + 2) , x ≠ -1
C. (f o g)^-1 (x) = (2x + 2) / (6x + 3) , x ≠ -1/2
D. (f o g)^-1 (x) = (2x - 2) / (3x + 6) , x ≠ - 2
E. (f o g)^-1 (x) = (3x - 6) / (2 - 2x) , x ≠ 1

Jawaban : E

f(x) = 3x - 5
g(x) = (4x + 7) / (2x + 3)

(f o g) (x) = 3 . (4x + 7) / (2x + 3) - 5
y = (12x + 21) / (2x + 3) - 5
y + 5 = (12x + 21) / (2x + 3)
(y + 5) (2x + 3) = 12x + 21
2xy + 3y + 10x + 15 = 12x + 21
2xy + 10 x - 12x = 21 - 15 - 3y
2xy - 2x = 6 - 3y
2x (y - 1) = 6 - 3y
x = (6 - 3y) / 2(y - 1)
x = (6 - 3y) / (2y - 2)

(f o g) (x)^-1 = (6 - 3x) / (2x - 2)
(f o g) (x)^-1 = - (3x - 6) / - (2 - 2x)
(f o g) (x)^-1 = (3x - 6) /(2 - 2x)

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