Question

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

• A. $\frac{3x}{\sqrt{1+x^{2}}}$
• B. $\frac{x}{\sqrt{1 + 3x^{2}}}$
• C. $\frac{3x}{\sqrt{1 - x^{2}}}$
• D. None of these

Answer 1

Answer: (B)

$\frac{x}{\sqrt{1 + 3x^{2}}}$

Answer 2

The correct answer is B:$\frac{x}{\sqrt{1+3x^2}}$
that;
$f(x)=\frac{x}{\sqrt{1+x^{2}}}$
$(f \circ f)(x)=\frac{\frac{x}{\sqrt{1+x^{2}}}}{\sqrt{1+\frac{x^{2}}{1+x^{2}}}}$
$=\frac{x}{\sqrt{2 x^{2}+1}}$
$(fofof)(x)=\frac{\frac{x}{\sqrt{2 x^{2}+1}}}{\sqrt{1+\frac{x^{2}}{2 x^{2}+1}}}$
$=\frac{x}{\sqrt{1+3 x^{2}}}$