Diketahui fungsi f(x)= 5x + 4,dan g(x)=2x+1/x-7, x≠7. Invers dari (fog) adalah…

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Diketahui fungsi f(x)= 5x + 4,dan g(x)=2x+1/x-7, x≠7. Invers dari (fog) adalah…
A. (fog) (x)= 7x -20/ x -13, ≠ 13
B. (fog) (x)= 7x+9/ x -10, ≠ 10
C. (fog) (x)= 7x -20/ x-13, ≠ 13
D. (fog) (x)= 7x -16/ x-10, ≠ 10
E. (fog) (x)= 7x -26/ x -13, ≠ 13

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1 Diketahui fungsi f(x)= 5x + 4,dan g(x)=2x+1/x-7, x≠7. Invers dari (fog) adalah… A. (fog) (x)= 7x -20/ x -13, ≠ 13 B. (fog) (x)= 7x+9/ x -10, ≠ 10 C. (fog) (x)= 7x -20/ x-13, ≠ 13 D. (fog) (x)= 7x -16/ x-10, ≠ 10 E. (fog) (x)= 7x -26/ x -13, ≠ 13
1.1 Rekomendasi Lain :

Jawaban:
(f o g)^(-1)(x) = (23 – 7y)/(14 – x); x ≠ 14

perhatikan konsep fungsi komposisi berikut:
(f o g)(x) = f(g(x))

perhatikan juga konsep invers fungsi berikut:
jika (f o g)(x) = y
maka inversnya: (f o g)^(-1)(y) = x

Diketahui:
f(x) = 5x + 4
g(x) = 2x+1/x-7, x≠7

Ditanya:
(fog)^(-1) (x) = ………?

Pembahasan:
(f o g)(x) = f(g(x))
(f o g)(x) = 5(g(x)) + 4
(f o g)(x) = 5(2x+1)/(x-7) + 4
(f o g)(x) = (10x+5)/(x-7) + 4(x – 7)/(x – 7)
(f o g)(x) = (10x+5)/(x-7) + (4x-28)/(x-7)
(f o g)(x) = [10x + 5 + 4x – 28]/(x-7)
(f o g)(x) = (14x – 23)/(x – 7)
(f o g)(x) = y

(14x – 23)/(x – 7) = y
(14x – 23) = y(x – 7)
(14x – 23) = xy – 7y
14x – xy = 23 – 7y
x(14 – y) = 23 – 7y
x = (23 – 7y)/(14 – y)

(f o g)^(-1)(y) = x
(f o g)^(-1)(y) = (23 – 7y)/(14 – y)
(f o g)^(-1)(x) = (23 – 7y)/(14 – x)
agar rasional, maka (14 – x) ≠ 0
(14 – x) ≠ 0
x ≠ 14

Jadi, invers dari (f o g)(x) adalah (f o g)^(-1)(x) = (23 – 7y)/(14 – x); x ≠ 14

Rekomendasi Lain :

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