# 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