Jika f(x)=1/(x-1), x=/=1 dan g(x)=x-2, maka (gof)^(-1)(x)=

(gof)^(-1)(x) = (3+x)/(x+2)

Pembahasan

Diketahui f(x) = 1/(x-1) dan g(x) = x-2. Pertama, kita cari (gof)(x) = g(f(x)) = g(1/(x-1)) = (1/(x-1)) - 2 = (1 - 2(x-1))/(x-1) = (1 - 2x + 2)/(x-1) = (3 - 2x)/(x-1). 
Selanjutnya, kita cari inversnya. Misalkan y = (3 - 2x)/(x-1). Maka y(x-1) = 3 - 2x -> yx - y = 3 - 2x -> yx + 2x = 3 + y -> x(y + 2) = 3 + y -> x = (3 + y)/(y + 2). 
Jadi, (gof)^(-1)(x) = (3 + x)/(x + 2).