f(×) = 3×+6/2×+5 g(×) = 3×-4 tentukan : (fog)-1 (x) =

oleh

f(×) = 3×+6/2×+5
g(×) = 3×-4
tentukan : (fog)-1 (x) =

Daftar isi : hide
1 f(×) = 3×+6/2×+5 g(×) = 3×-4 tentukan : (fog)-1 (x) =
1.1 Rekomendasi Lain :

Jawaban : (fog)¯¹(x) = (3x – 6) / (6x – 9)

Perhatikan penjelasan berikut ya.

Ingat kembali :
(fog)(x) = f(g(x))
(gof)(x) = g(f(x))
f(x) = y —–> f¯¹(x) = x

Diketahui : f(x) = (3x + 6) / (2x + 5) dan g(x) = 3x – 4

Ditanya : (fog)¯¹(x) = … ?

Maka :
(fog)(x) = f(g(x)
(fog)(x) = f(3x – 4)
(fog)(x) = [3(3x – 4) + 6] / [2(3x – 4) + 5]
(fog)(x) = (9x – 12 + 6) / (6x – 8 + 5)
(fog)(x) = (9x – 6) / (6x – 3)

Sehingga:
(fog)(x) = (9x – 6) / (6x – 3)
y = (9x – 6) / (6x – 3)
y(6x – 3) = 9x – 6
6xy – 3y = 9x – 6
6xy – 9x = -6 + 3y
x(6y – 9) = 3y – 6
x = (3y – 6) / (6y – 9)
(fog)¯¹(x) = (3x – 6) / (6x – 9)

Jadi, (fog)¯¹(x) = (3x – 6) / (6x – 9).

Rekomendasi Lain :