Question

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

• A. $\frac{x}{\sqrt{1-x^2}}$
• B. $\frac{x}{\sqrt{1-2x^2}}$
• C. $\frac{x}{\sqrt{1-3x^2}}$
• D. $x$

Answer 1

Answer: (B)

$\frac{x}{\sqrt{1-2x^2}}$

$fof\left(x\right)=f\left(f\left(x\right)\right)=\left(x/\sqrt{1-x^2}\right)/\left(\sqrt{1-\left(x^2/(1-x^2)\right)}\right)$
$=\left(x/\sqrt{1-x^2}\right)/\sqrt{(1-x^2-x^2)/(1-x^2)}$
$=\left(x/\sqrt{1-x^2}\right)/\left(\sqrt{1-2x^2}/\sqrt{1-x^2}\right)$
$=x/\sqrt{1-2x^2}$