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Let \(f(x) = \frac{x}{\sqrt{1 + x^2}}\)

A sequence of functions is defined by \(f^{(1)}(x) = f(x)\) and

 \(f^{(n)} (x) = f(f^{(n - 1)}(x))\) for \(n \ge 2\) find \(f^{(99)}(1)\)

 

tyyy laugh

 Nov 27, 2021
 #1
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f^1 (1) = 1/sqrt(2)

f^2 (1) = 1/sqrt(3)

f^3 (1) = 1/sqrt(4)

 

Do you see a pattern?

I hope this helped. :))

 

=^._.^=

 Nov 28, 2021

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