Întrebare compozitie

Buna ziua
\[fie f:R-\{1\}\rightarrow R,f(x)=\dfrac{3x+1}{1-x}\\ Sa\ se\ determine\ \underbrace{f\circ f\circ f\circ f\dots\circ f}_{f\ de\ 2016\ ori}(4)\\ a)-\dfrac{2015}{2016};b)-\dfrac{5011}{5009};c)-\dfrac{5044}{5039};\\ d)-\dfrac{2021}{2120};e)-\dfrac{5023}{5021}\]

multumesc
Indicatie:Se pleaca de la matricea:
\[A(x)=\begin{pmatrix}3&1\\ -1&1\\ \end{pmatrix}\ apoi\ A^2(x)=\begin{pmatrix}8&4\\ -4&0\\ \end{pmatrix};\\A^3(x)=\begin{pmatrix}20&12\\ -12&-4\\ \end{pmatrix}; A^4(x)=\begin{pmatrix}48&32\\ -32&-16\\ \end{pmatrix}\\ iar\ la\ fel\ f(x)=\dfrac{3x+1}{1-x};(f\circ f)(x)=\dfrac{8x+4}{-4x};\\ (f\circ f\circ f)(x)=\dfrac{20x+12}{-12x-4};(f\circ f\circ f\circ f)(x)=\dfrac{48x+32}{-32x-16};etc.\]
Se observa potrivirea de cifre.
Mai departe cum obtin A^2016?Prin recurenta sau inductie?
multumesc
PS :Problema a fost rezolvata la acest capitol cu ocazia calcularii
"Puterea unei matrice".