Q60 / 125 · BITSAT 2010 · Mathematics

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

  • A
    \(\frac{3 x}{\sqrt{1+x^2}}\)
  • Correct answer
    B
    \(\frac{\mathrm{x}}{\sqrt{1+3 \mathrm{x}^2}}\)
  • C
    \(\frac{3 x}{\sqrt{1-x^2}}\)
  • D
    None of these

Solution

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

Hence, the correct answer is option: 'B'.

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