Question

If $f\left(x\right)=\frac{x}{\sqrt{1-x^2}},g\left(x\right)=\frac{x}{\sqrt{1+x^2}}$, then $\left(fog\right)\left(x\right)=$

• A. $x$
• B. $\frac{x}{\sqrt{1+x^2}}$
• C. $\sqrt{1+x^2}$
• D. $2x$

Answer 1

The correct option is A $x$

$fog\left(x\right)=f\left(g\left(x\right)\right)$
$=f\left(\frac{x}{\sqrt{1+x^2}}\right)$
$=\frac{\frac{x}{\sqrt{1+x^2}}}{\sqrt{1-\frac{x^2}{1+x^2}}}=x$