Turtles all the way

Calculus Level 4

Consider a function \(f(x) \) that satisfies

  • \(f'(x) = \dfrac{1}{x + \dfrac{1}{x + \dfrac{1}{...}}}\), and
  • \(f(0) = 0\).

What is all of the possible values of \(f(3)\) (to 2 decimal places)?

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