Bounding functions

Algebra Level 4

Functions \( f : [1, \infty) \rightarrow [1, \infty) \) satisfy:

  1. \( f(x) \leq 2(1+x), \ ∀ x \in [1, \infty) \)

  2. \( xf(x+1) = f(x)^2 - 1, \ ∀ x \in [1, \infty) \)

Find all possible values of \( f(2014) \).

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