Jika f(x) = (x-2011)/(x-1), maka (fofofofof)(x) = .....

Jawaban yang benar adalah (x-2011)/(x-1) Konsep : Komposisi dua fungsi : (fog)(x)= f(g(x)) Pembahasan : f(x) = (x-2011)/(x-1) (fof)(x) = f(f(x)) = f((x-2011)/(x-1)) = ((x-2011)/(x-1) – 2011)/((x-2011)/(x-1) – 1) = ((x-2011)/(x-1) – 2011(x-1)/(x-1))/((x-2011)/(x-1) – (x-1)/(x-1)) = ((x-2011)/(x-1) – (2011x-2011)/(x-1))/((x-2011-(x-1))/(x-1)) = ((x-2011-(2011x-2011))/(x-1))/((x-2011-(x-1))/(x-1)) = ((x-2011-2011x+2011)/(x-1))/(x-2011-x+1))/((x-1)) = ((-2010x)/(x-1))/((-2010)/(x-1)) = ((-2010x)/(x-1)) · ((x-1)/(-2010)) = (-2010x)/(-2010) = x Sehingga : (fofof)(x) = f((fof)(x)) = f(x) (fofofof)(x) = f((fofof)(x)) = f(f(x)) = x (fofofofof)(x) = f((fofofof)(x)) = f(x) = (x-2011)/(x-1) Jadi diperoleh komposisi fungsi (fofofofof)(x) = (x-2011)/(x-1)