F(x) = tentukan (f o f o f o f o f)(x)

F(x) =
tentukan (f o f o f o f o f)(x)

Jawab:

$frac{x+2011}{x-1}$

Penjelasan dengan langkah-langkah:

$f(x)=frac{x+2011}{x-1}$

Jadi:

$(fof)(x)=f(f(x))\=frac{frac{x+2011}{x-1} +2011}{frac{x+2011}{x-1}-1 } \=frac{frac{x+2011}{x-1} +frac{2011x-2011}{x-1} }{frac{x+2011}{x-1} -frac{x-1}{x-1} } \=frac{frac{2012x}{x-1} }{frac{2012}{x-1} } \=x$

Akibatnya

$(fofofofof)(x)=(fofof)(f(f(x)))\=(fofof)(x)\=f(x)\=frac{x+2011}{x-1}$

Semoga Membantu^^