Devil Maths

Algebra Level 4

Let f(x)=x1+x2f(x)=\dfrac{x}{\sqrt{1+x^2}} .

Define f(n)(x)=f(f(f(x)))f^{(n)}(x)=f(f(\cdots f(x))), that is ff composed with itself nn times.

Find f(99)(1)f^{(99)}(1).

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