If (f(x)= x 1+x^2 ), then (fof of )(x) is

If (f(x)=\frac{x}{\sqrt{1+x^2}}), then (fof of

)(x)

Options

A(\frac{3 x}{\sqrt{1+x^2}})
B(\frac{\mathrm{x}}{\sqrt{1+3 \mathrm{x}^2}})
C(\frac{3 x}{\sqrt{1-x^2}})
DNone of these

Correct answer

B. (\frac{\mathrm{x}}{\sqrt{1+3 \mathrm{x}^2}})

Step-by-step solution

(\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{\sqrt{1+\mathrm{x}^2}}) ((f o f)(x)=\frac{\frac{x}{\sqrt{1+x^2}}}{\sqrt{1+\frac{x^2}{1+x^2}}}=\frac{x}{\sqrt{2 x^2+1}}) ((fofof)(x)=\frac{\frac{x}{\sqrt{2 x^2+1}}}{\sqrt{1+\frac{x^2}{2 x^2+1}}}=\frac{x}{\sqrt{1+3 x^2}})

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