Find all functions $f:[1,\infty )\rightarrow [1,\infty)$ satisfying the following conditions: (1) $f(x)\le 2(x+1)$; (2) $f(x+1)=\dfrac{1}{x}[(f(x))^2-1]$ .
Problem
Source: China Mathematical Olympiad 1994 problem3
Tags: function, inequalities, algebra unsolved, algebra