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Calculus Level 4

The sequence of functions defined by

\( f_0: x \mapsto \sqrt{x} \)

\( f_{n+1}: x \mapsto \sqrt{x+\sqrt{x-f_n}} \)

converges absolutely in the valid domain and codomain as \( n \to \infty \)

The domain and codomain of the sequence of functions are both \(\mathbb{R}^+\)

Which function does it converge towards?

Bonus: Determine the domain and range of \(f_\infty\)


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