Question

I f $f:R\to R$ s defined by $f\left(x\right)=\frac{x}{x^2+1}$, find $f\left(f\left(2\right)\right)$.

• A. $29/9$
• B. $29/8$
• C. $29/10$
• D. $10/29$

Answer 1

Answer: (D)

Given $f\left(x\right)=\frac{x}{x^2+1}$
$\Rightarrow f\left(2\right)=\frac{2}{2^2+1}=\frac{2}{5}$
$\Rightarrow f\left(f\left(2\right)\right)=f\left(\frac{2}{5}\right)=\frac{\frac{2}{5}}{{\left(\frac{2}{5}\right)}^2+1}$
$=\frac{\frac{2}{5}}{\frac{4}{25}+1}$
$=\frac{\frac{2}{5}}{\frac{29}{25}}$
$=\frac{10}{29}$.