Diketahui f(x)= 2x/(3x-1) dan g(x)=4x+1. Tentukan :

Jawaban:

f(x) = 2x / 3x – 1

g(x) = 4x + 1

(g-¹ o f-¹ )(x) = (gof)-¹(x)

Pertama, cari (gof)(x)

(gof)(x)

= 4(2x / 3x – 1) + 1

= 8x / 3x – 1 + 1

= 8x / 3x – 1 + 1(3x – 1 ) / 3x – 1

= 8x + 3x – 1 / 3x – 1

= 11x – 1 / 3x – 1

misal (gof)(x) = y

y = 11x – 1 / 3x – 1

y( 3x – 1 ) = 11x – 1

3xy – y = 11x – 1

3xy – 11x = y – 1

x ( 3y – 11 ) = y – 1

x = y – 1 / 3y – 11

(gof)-¹(x) = x – 1 / 3x – 11