If $ f(x)=\frac{x}{\sqrt{1+x^{2}}} $, then $ (f o f o f)(x) $ is

Question

If $ f(x)=\frac{x}{\sqrt{1+x^{2}}} $, then $ (f o f o f)(x) $ is, $ \frac{3 x}{\sqrt{1+x^{2}}} $, $ \frac{x}{\sqrt{1+3 x^{2}}} $, $ \frac{3 x}{\sqrt{1-x^{2}}} $, none of these

MARKS App · Accepted Answer

Given: f x = x 1 + x 2 Then, f o f x = f f x = f x x 2 + 1 = x 1 + x 2 1 + x 2 1 + x 2 = x 2 x 2 + 1 f o f o f x = f f f x = f x 2 x 2 + 1 = x 2 x 2 + 1 1 + x 2 2 x 2 + 1 = x 1 + 3 x 2

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