Q39 / 100 · BITSAT 2023 (Memory Based Paper 1) · Mathematics
If $f(x)=\frac{x}{\sqrt{1+x^2}}$, then (fof of) $(x)$ is
- A$\frac{3 x}{\sqrt{1+x^2}}$
- Correct answerB$\frac{x}{\sqrt{1+3 x^2}}$
- C$\frac{3 x}{\sqrt{1-x^2}}$
- DNone of these
Solution
$f(x)=\frac{x}{\sqrt{1+x^2}}$
fof$=\frac{\frac{x}{\sqrt{1+x^2}}}{\sqrt{1+\frac{x^2}{1+x^2}}}=\frac{x}{\sqrt{2 x^2+1}}$
fofof $=\frac{\frac{x}{\sqrt{2 x^2+1}}}{\sqrt{1+\frac{x^2}{2 x^2+1}}}=\frac{x}{\sqrt{1+3 x^2}}$
fof$=\frac{\frac{x}{\sqrt{1+x^2}}}{\sqrt{1+\frac{x^2}{1+x^2}}}=\frac{x}{\sqrt{2 x^2+1}}$
fofof $=\frac{\frac{x}{\sqrt{2 x^2+1}}}{\sqrt{1+\frac{x^2}{2 x^2+1}}}=\frac{x}{\sqrt{1+3 x^2}}$
Hence, the correct answer is option: 'B'.