Diketahui Fungsi f(x) =2x – 3 dan g(x) =1/3x + 1 ,X≠-1/3 , tentukan (gof)-¹(x) !

Penjelasan dengan langkah-langkah:

Diket :

f(x) = 2x – 3 dan g(x) = 1 / (3x + 1)

Tentukan fungsi invers (gof)⁻¹(x) !

Jawab :

(gof)(x) = g(f(x))

(gof)(x) = 1 / (3(2x – 3) + 1)

(gof)(x) = 1 / (6x – 8)

y = 1 / (6x – 8)

y(6x – 8) = 1

6xy – 8y = 1

6xy = 8y + 1

x(6y) = 8y + 1

x = (8y + 1)/6y

(gof)⁻¹(x) = (8x + 1)/6x

Semoga Bermanfaat