diketahui f(x) = 2x+1/x-1 , x=1 dan g(x) = 3x + 1 invers fungsi (fog)(x) adalah

Mapel : Matematika
Materi : Fungsi Komposisi, Invers
Kelas : 10


f(x) = (2x + 1)/(x - 1)
g(x) = 3x + 1

(f o g) (x) :
= f(3x + 1)
= [2(3x + 1) + 1] /[(3x + 1) - 1]
= (6x + 3) / 3x

Misalkan,
(6x + 3)/3x = y
6x + 3 = 3xy
6x - 3xy = -3
3xy - 6x = 3
x(3y - 6) = 3
x = 3/(3y - 6)


Sehingga :
(f o g) -¹(x) = 3/(3x - 6)