na.numerical analysis – Solving equation for higher degree of composition


Given this function f(x) = x – 1/x .

the equation f(f(x)) = x has two solutions : $frac{1}{sqrt{2}}$, $frac{-1}{sqrt{2}}$ , but how about solving this equation for a higher degree of composition , for example f(f(….(f(x)))) = x ( 15 times ) , what is the mathematical tool needed in order to solve this equation